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временный
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1. The
T
between vowels is a Flap
T
.
2. Area divided by delta
t
is constant at our time.
3. is less than or equal to
t
, which
4.
t
is e to the
t
plus cosine
t
. And that is the same answer as
5. So for any epsilon, for any
t
and for any epsilon,
6. And given that time
T
, then stock price is S_T.
7. So that's basically, remember the
t
distribution
8. So I always think,
T
-H-I-N-K,
T
-H-I-N-K, remember that.
9. and minus q alpha over 2 of
t
minus 1.
10. Well, this thing, remember Fn of
t
by definition was--
11. If I give you a parametric curve, sin
t
,
12. That means, in particular, we take the limit as delta
t
13. to have a
t
distribution.
14. So really the
t
here is F of the original one.
15. That means, in particular, we take the limit as delta
t
16. hey, why don
t
you queen up your act?
17. and variance 1 at
t
equals plus infinity.
18. And that's just for any given
t
.
19. Second syllable stress. da-DA-da-da. Thermometer. Thermometer. Flap
T
.
20. So if you think about a map, how does the
t
21. Everybody sees that this
t
here is not the same as this
t
here?
22. So I look at the graph
T
. I Know
T
is connected.
23. so I'm going to look at
t
between 0
24. Let's call it w of
t
as
t
increases.
25. KT: K-E-
T
-E-L-Y-N
26. subgraph
T
, essentially, with a smaller number of edges.
27. So that's my
t
distribution.
28. AUDIENCE: Question, f of
t
[INAUDIBLE]?
29. It means this thing is proportional to delta
t
.
30.
T
star could be, for example, the spanning tree
31. The number "three",
t
-h-r-e-e is often pronounced
32. So let's move on to Student's
t
-test.
33. F of
t
, exactly.
34. as
t
changes? Well, it stays constant because
35. delta
t
. So, let's zoom into that curve.
36. time
t
equals zero when the point is not moving.
37. depend on
t
, and then you can find the rate
38. have a couple options with the
T
in ‘get’. You can either make it a flap
T
, connecting
39. sin(
t
) is 0. The velocity is 0.
40. BV/KT: (FS)
T
-H-A-N-K Y-O-U
41. so F of
t
is the probability that X
42. I would read this as sup over
t
of Fn
t
minus F of
t
43. And
T
, capital
T
, stands for the future time.
44. What could happen is that for
t
equals 1
45. do a linear regression
t
-test, we are going to be doing those
t
-tests on the slope. And
46. for the stock at time
T
?
47. function which is equal to
t
for
t
between 0 and 1?
48. We know that this particular
T
over here
49. of
t
. I mean, really,
50. KT: (FS)
T
-H-A-N-K-S
51.
T
-that being these things.
52. What can you tell me about that
T
? Grater.
53. minus F of
t
exceeding delta is less than epsilon
t
.
54. The
T
in HOT is followed by a consonant. Make that a Stop
T
.
55. [
T
] However, your job isn't over just yet.
56. a little bit by delta
t
. We will actually use the
57. You could answer based on that. See, at
t
equals 0,
58. r equals r of
t
, that stays inside,
59. dr/ds should be
T
. Well, let's think of dr/ds.
60. It's that K or it's this
T
or it's
61. This is the equation
T
times u divided by h squared
62. changes in x, y, z in a small time delta
t
.
63. hat minus sup over
t
, I get something
64. trajectory. So, the usual notation is
T
hat.
65. What do you notice about the double
T
?
66. Two words: one ending with a '
t
',
67. DENNIS FREEMAN: f of
t
was the original signal.
68. And, what do you do? En, what doet u? It's onlt w a
t
, w a
t
, wat. En, what doet u? En,
69. variables on
t
, then it becomes just a function
70. x is
t
and y is e^
t
, so that will be 2t e to the
t
,
71. functions of a variable
t
. And then you do the
72. The point is not moving. At
t
equals pi,
73. Remember w was x^2y z. x was
t
, so you get
t
squared,
74. with a "
t
" in it, the "
t
" is not pronounced. So, some... A lot of Cockney speakers will
75. argument with a single argument of type
T
.
76. Sorry, at
t
is equal to infinity.
77. KT:
T
-H-A
78. can substitute
t
instead of x, y, z.
79. and smaller values of delta
t
then these ratios of numbers
80. the next one starting with a '
t
',
81. [
T
] Begin audio prompt in 3...2...1.
82. When we take the limit, as delta
t
tends to zero,
83. PROFESSOR: F of
t
, right?
84. And a
t
distribution is basically
85. y is e to the
t
, plus z was sine
t
.
86. So is anybody a
t
-test kind of person?
87. of
t
then dx is x prime of
t
dt, dy is y prime of
t
dt,
88. En, wat doet u? It's w a
t
, w a
t
. Ik ben een student. student.
89. So a variance 0 at
t
equals plus infinity,
90. because at negative infinity F of
t
is going to 0.
91. That's the number 7, S-
T
-E-P-S.
92. So when you go from
t
to just
t
a little after that,
93. will get an MIT chemistry
T
-shirt.
94. For any given
t
, the average converges to the true.
95. what's the derivative of one minus cos(
t
)?
96.
t
equals zero. But, it's a convention.
97. this is the area swept in time delta
t
.
98. and variance-- sorry, at
t
equals negative infinity,
99. Do I have the same thing uniformly in
t
?
100. because what is the variance of Fn of
t
minus F of
t
at
t
is
101. KT: how sign
T
-H-A-N-K-S?
102. And so now for
t
between 0 and 1, then
103. to the
t
variable in the second problem?
104. I think, or something like that, 3.55 for
t
.
105. tells me that for any given
t
, if n is large enough, Fn of
t
106. OK so, those guys, Fn of
t
, this guy
107. And what the
t
statistic is doing
108. which is F of
t
.
109. Here
t
stands for instantaneous time.
110. BV & KT: (both fingerspell) K-A-
T
-E-L-Y-N
111. is for
t
in the entire real line.
112. But I assumed that
T
was already the smallest
113. At the end of calculation we get 2t e to the
t
plus
t
squared
114. if I look only at the
t
-th one, it
115. And let me use a capital
T
for transpose.
116.
T
.
T
because the top boundary condition is free.
117. But it's
T
, that's the important thing.
118. to build because you have to take the supremum over
t
.
119. And
t
is just basically instantaneous time.
120. [Sings] Idon
t
wanna do the..
121. the quantiles of a Gaussian distribution or a
t
122. e to the
t
plus cosine
t
. That is what the chain rule
123. And that's just for any given
t
.
124. interval, delta
t
. In time, delta
t
,
125. So let
T
star be such a minimum spanning tree.
126. So what is
T
star?
127. And so what we know is that Fn of
t
goes to F of
t
128. The sound you just heard was f of
t
.
129. That’s right. Another Flap
T
. The -ing ending is unstressed.
130. r. The other one is v delta
t
.
131. Just like ‘butter’, it’s a Flap
T
. Not tt, a True
T
.
132. maybe that n of
t
is something that looks like
t
.
133. It's some random variable that's indexed by
t
.
134. For any epsilon in
t
we know we have this.
135. So that's
T
divided by h squared.
136. For the marginal distributions at each instance
t
,
137.
t
-shirt ah but the baby is wearing
138. The
T
is between vowels, so it’s a Flap
T
.
139. And as
t
goes to plus infinity, F of
t
140. situation where x is a function of
t
, y is a function of
t
and z
141. [
T
] Begin audio prompt in 3...2...1.
142. actually, on four variables, x, y, z,
t
.
143. So we constructed
T
as the subgraph that
144. some variable,
t
,
145. [
T
] Document results.
146. So it says, for all epsilon and all
t
,
147. that are less than
t
.
148. OK so, those guys, Fn of
t
, this guy
149. it's less than 0, which is 1/2, so
t
only
150. times delta
t
. I can take out the delta
t
,
151. has some normal distribution with variance
t
.
152. it's going to be square root of 1 - 2cos(
t
) cos^2(
t
) sin^2(
t
).
153. so F of
t
is the probability that X
154. should be close to F of
t
.
155. for
t
in the entire real line, this guy
156. Sorry, at
t
is equal to infinity.
157. is actually equal to the minimum of s and
t
.
158. I made that ending
T
a Stop
T
. Trivet.
159. AUDIENCE: f of minus
t
.
160. KT:
T
161. So why not use the
t
test?
162. follows some distribution which is N 0,
t
minus s.
163. here? Then, 1- cos(
t
) is 0,
164. I have that are less than
t
.
165. So, we have r at time
t
. We have r at time
t
plus delta
166. of
t
1 minus F of
t
structure?
167. [
T
] Begin audio prompt in 3...2...1.
168. is 1- cos(
t
). The derivative of 1 is 0.
169. DENNIS FREEMAN: f of minus
t
--
170. you're right, the variance is F of
t
1 minus F of
t
.
171. that X is less than or equal to
t
.
172. My
t
distribution with n minus 1 degrees of freedom.
173. when
t
goes to infinity the Brownian bridge
174. That's the first pivot P-I-V-O-
T
. Pivot.
175. People use only
t
tests, right?
176.
T
(1, 1) = 1.
177. And that's a
t
distribution with d degrees of freedom.
178. BV: hey, hey how you sign (fingerspells)
T
-H-A-N-K-S, (FS)
T
-H-A-N-K-S
179. It could be the case that for each given
t
,
180. two means. And I finished the video with examples of doing a
t
-sample mean
t
-test and a 2 sample
181. delta
t
tends to zero. That means if I choose smaller
182. Now, is the following sound minus f of
t
.
183. As a function of this
t
here?
184. Oh, wow. It's like a big chocolate
T
.
185. So number one,
t
-tests are like a statistical analysis.
186. so I look at square root of n Fn of
t
,
187. counting how many observations they have that are less than
t
.
188. of n Fn of
t
minus F of
t
, sorry, F0 of
t
.
189. exceeds q alpha over 2 of
t
n minus 1.
190. It's minus phi of
t
over 2.
191. I want to do
T
-H-I-N--
192. You should think of delta
t
as relatively small.
193. want this to hold for all
t
at the same time.
194. Fn of
t
goes to F of
t
.
195. So if square root of n absolute value of Fn of
t
minus F of
t
196. has a
t
distribution with n minus 1 degrees of freedom.
197. And I hope that for all t's, Fn of
t
198. Can I write something that holds uniformly in
t
?
199. degree of freedom, and looking at the
t
score...
t
-star... critical value for being 95% confident
200. So Fn of
t
looks like this.
201. some number q alpha over 2 of
t
n minus 1
202. But we actually defined what a
t
distribution was.
203. one third of f of
t
?
204. The double
T
comes between two vowel sounds.
205. AUDIENCE: F of
t
.
206. And so this is equal to
t
.
207. dx over dt is one plus x squared is
t
squared,
208. And, that's also the position vector r of
t
.
209.
t
times the vector v. It gives you x,
210. for the stock at time
t
.
211. of
t
, that comes from this guy.
212. The fact that Fn of
t
converges to F of
t
for all
t
,
213. The type
T
is inferred for the function call,
214. And, delta r is approximately
T
times delta s.
215. That the n that depends on
t
, there's actually one largest n
216. remember to
T
-H-I-N-K. Remember to think.
217. that 2 phi minus N 0, 1, is less than
t
.
218. Or maybe, well, integer part of
t
.
219. and
t
, such that the probability that Fn
t
220. times e to the
t
plus
t
squared time the derivative of e to the
221. Which is equivalent to saying that Fn of
t
minus F of
t
as n
222. r, and v delta
t
, magnitude of the cross product.
223. is a function of
t
. That means you can plug in
224. It's
T
ds/dt. So, maybe if I actually stated
225. So the whole graph
T
is much bigger, right?
226. I'm going to call it
T
. So all the other guys
227. I..."That's a funny one, isn't it? "o-u-g-h-
t
"
228. It's not like Student
t
test allows you to get rid
229. dy over dt is e over
t
, plus dz over dt is cosine
t
.
230. We know that
T
is not a spanning tree.
231. So therefor,
T
must have a cycle.
232. Or maybe, well, integer part of
t
.
233. The variance goes from 0 at
t
is negative infinity,
234. It's sin(
t
). And, what's the derivative of
235. Let's divide everybody by delta
t
.
236. There B double O
T
Y
237. Notice I pronounced this with a Stop
T
. Plate.
238. be
t
, y will be e^
t
and z will be sin(
t
).
239. times delta
t
, OK, and just using the
240. I will get back the original
T
over here.
241. parameter rather than
t
. Well, it's a convention.
242. BV/KT: (FS)
T
- H-A-N-K-S
243. AUDIENCE: F of
t
.
244. The derivative of -cos(
t
) is sin(
t
).
245. should be close to F0 of
t
.
246. It's just an n that depends on
t
.
247. AUDIENCE: If you were to have minus f of
t
,
248. I would create K, I would take
T
equal K,
249. our planet moves by v delta
t
, OK?
250. sin(
t
)? cos(
t
), OK.
251. of
t
over 2.
252. [Mark whimpers "Why?"] [
T
] Of course,
253. Since
T
is reified or real, you can
254. substitute. W as a function of
t
.
255. So it means that for any a
t
and delta,
256. f sub y y prime of
t
dt plus f sub z z prime of
t
dt.
257. Can I write something that holds uniformly in
t
?
258. It just happens that this random variable is indexed by
t
,
259. KT: (FS)
T
-H-A-N-K-Y-O-U
260. What I'm finding is, for this
t
distribution,
261. well, the probability that something is less than
t
262. [
T
] Begin audio prompt in 3...2...1.
263. Similarly, here delta x over delta
t
, when delta
t
is really
264. it converges at a certain rate, and for
t
equals 2
265.
t
. This vector here I will call
266. PROFESSOR: For all epsilon and all
t
.
267. The double
T
is a Flap
T
again. Bottle opener.
268. by
t
.
269. But then maybe it's an n of
t
.
270. w equals c. So, it's zero because w of
t
271. a tree, and
T
is not a tree.
272. And the reason why you see
t
test
273. KT: how sign
T
-H-A-N-K Y-O-U
274. it's going to say
t
test.
275. the graph
T
minus this edge e is still connected.
276. actually functions of one variable
t
.
277. So it's F of
t
1 minus F of
t
.
278. For any epsilon in
t
we know we have this.
279. for all
t
.
280. parameters
t
. But, actually,
281. And here is an MIT chemistry
T
-shirt.
282. So if this n is just
t
, maybe
t
over epsilon,
283. Well, you'd have to basically integrate this quantity from
t
284. but since everything depends on F of
t
,
285. So for all
t
you have a Gaussian distribution.
286. Girl: (fingerspells) K-A-
T
-E-L-Y-N
287. find the position, so, x of
t
, y of
t
,
288. after removing e from
T
.
289. of change with
t
of a value of f.
290. Could be AT&
T
and so on and so forth.
291. Which are now to be at time capital
T
.
292. "s", "
t
", "d", "f".
293. And this is where the sup for
t
in R of Fn of
t
.
294. KT: K-A-
T
-E-L-Y-N
295. Here, I pronounced the final
T
as a True
T
. Cookie sheet. Tt- tt-
296. temperature for point x, y, z at time
t
.
297. variable
t
. Now, of course,
298. So for
t
distribution that's definitely
299. [
T
] Document results.
300. It is the equation partial f over partial
t
equals some
301. The supremum over
t
, again in R, so this guy is
302. to get the function d of
t
.
303. Since Kotlin can figure out the type of
T
based entirely
304. what is the distribution at each instant
t
.
305. I pronounced the ending
T
as a Stop
T
.
306. What is this
t
here?
307. formula there? Well, so, the derivative of
t
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