2.5.8) Suppose that Y is a continuous random variable whose pdf is given by f(x) = {K (4y = 2 (K(4y-2y²), 0 1). (c) Find F(y).
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- 3.2.13 Y is a continuous random variable with { 2(1- y), 0< y < 1; fy(4) = { 0, otherwise. Derive Fy(t).Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?34. Consider the continuous random variable X whose pdf is given by f(r) = (a-r³)Io<<1(1). (a) Find the value of a that makes f(z) a pdf. (b) Find E(X). (c) Find V(X). (d) Find P(X ≤).
- a) You throw two fair dice labeled 1, . . . , 6 independently of each other and let X be the minimum of the two results. Calculate E[X2]. (b) Suppose that X has pdf given by f(x) = 3x^(−4) if x > 1 and by f(x) = 0 if x <= 1. Calculate the median of X.2.4.1. Show that the random variables X, and X2 with joint pdf f(x1, r2) = { 1201 *2(1- 2) 0 < x1 < 1, 0< x, < 1 12x122(1 – x2) 0< x1 < 1, 0 < x2 < 1 elsewhere are independent.For each of the following functions, (i) find the constant c so that f(x) is a pdf of a random variable X,(ii) use the definition to find the cdf, F (x) = P (X < x).(a) f (x) = 15(x^4)/32 , −c < x < c(b) f (x) = c/(x^(1/3)) , 0 < x < 8 Is this pdf (probability distributive function) bounded?
- 3. Consider two random variables X₁ and X2 whose joint pdf is given by for x₁0, x2 > 0, x₁ + x2 < 2, { Find the pdf of Y = X₂ - X₁. f(x1, x₂) = NIT otherwise.3 Let X be the number of siblings of WSU students. The pdf of X is: f(x) = (5-x)/15 for x = 0, 1, 2, 3, 4 What is the probability that a randomly selected student has 3 or more siblings if it is known that they are not an only child X 0.133 X 0.2 / 0.3 O X 0.667 X 0.9335.5.5 X and Yare random variables with the joint PDF S5x²/2 fx,x (x, y) - otherwise. (a) What is the marginal PDF fx(x)? (b) What is the marginal PDF fy(y)?
- (c) What is the asymptotic distribution of √n(0-0)? 6.2.9. If X1, X2,..., Xn is a random sample from a distribution with pdf ={ f(x; 0) = 303 (x+0)4 0 0Thank you7. a) Suppose that X is a uniform continuous random variable where 0SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON