1) Let the probability function of a discrete random variable X be 100) = {(²+²) (0.5) (05) 1-², (0.5)*(0.5 f(x) 0, *(0.5) 16-x, for x = 0,1... 16 elsewhere a) Find the exact value of P(IX-ul < 20). b) What is the approximate value of P(|X-μ| <20)?

Q: (52) Let X be a random variable with p.d.f. 1 5 0 <x<0 5 2 f(x) =- find E(e3 ) O.W

A: Given, X is a random variable with pdf- fx=15e-15x  ;0&lt;x&lt;∞0            ; otherwise

Q: a) Show that the following function is a valid probability mass function of the random variable X.…

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Q: (b) Let a discrete random variable X have the following PMF: p(x) = k (=) , for x = 1,2, . ..; 0,…

A: Basic probability

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A: X=3 X=4 X=5 X=6 Total Y=4 7114 8114 9114 10114 34114 Y=5 8114 9114 10114 11114 38114…

Q: Let f(x) is probability function of discrete random variable x then Σικ) 1 صواب

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Q: 2. Let X₁, X₂₁.... X ₁ be a i.i.de Sequence of random variables. Show that Cov (X₂X₁ X) = 0₁ V₂ =…

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Q: L3. Let X₁,..., X10 P(E(X₁) > > 0.5). N(0, 1). Determine the probabilities P(X₁ > 0.5), P(X > 0.5)…

A: The provided information is as follows:It is given that we have the random variables  which follow a…

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A: Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

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Q: =4, H1:8-9. show that the sequential probability ratio test car statistic X7, with a=0.05 and…

A: *Answer:

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Q: Let X denote a random variable that takes on any of the values -1, 0, 1 with respective…

A: P(X = −1) = 0.2,P(X = 0) = 0.5,P(X = 1) = 0.3.

Q: Find the probability !is pad.f. (2x+1) 15 x=1,2,3 p(x) = elsewhere

A: given p.d.f  p(x)=115(2x+1)   x = 1,2,3

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Q: 24. Let X1, X2, .., X 100 be a random sample of size 100 from a distribution with density S(2) = {6…

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Q: 20) Let X be a random variable with p.d.f. k T<x<10 f(x) =- , find k. O.w

A: Solution: Let X be the random variable with pdf f(x) is  f(x)=kx       1&lt;x&lt;100      otherwise

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A: Given: f(x)=2(1-x) , 0&lt;x&lt;1 The formula to compute the mean is: V(x)=∫x2fx dx-∫xfx dx2

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Q: Find the standard deviation of the random variable X using any method

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Q: 14- If the p. d. f of a random variable X is f(x) = 2,0 ≤ x ≤ 2, then P(X> 1.5|X > 1) is (a) 0.5833…

A:

Q: 2) Required probability is given by 99 P(X 2 100) = 1 - (C")-0.01°- 0.99-3 = 1 - 0.0092427 0.990757…

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Q: Let X be a random variable with p.d.f. 1<x<0 f(x) =- find k. O.W

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Q: S. P(S = s) = fs(s) = {1+11+ ; s= 0,1,2, %3D %3D %D 0; e.w.

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Q: (7) Let X be a random variable with p.d.f. 1<x<0 f(x) = { ,find k. O.W

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Q: (i) Show that c = 2 (ii) Calculate the mean and variance of X. (iii) Find the CDF of the random…

A: As per policy I have calculated first 3 subparts plz REPOST for remaining parts with note I need…