(b) ONLY! Though you can use the result from (a) without proof
(b) ONLY! Though you can use the result from (a) without proof (a) Let F(x) =...
3. Let {X1, X2, X3, X4} be independent, identically distributed random variables with p.d.f. f(0) = 2. o if 0<x< 1 else Find EY] where Y = min{X1, X2, X3, X4}.
6. Let X1, X2,.. , Xn denote a random sample of size n> 1 from a distribution with pdf f(x; 6) = 6e-8, 0<x< 20, zero elsewhere, and 0 > 0. Le Y = x. (a) Show that Y is a sufficient and complete statistics for . (b) Prove that (n-1)/Y is an unbiased estimator of 0.
Let > 0 and let X1, X2, ..., Xn be a random sample from the distribution with the probability density function f(x; 1) = 212x3 e-tz, x > 0. a. Find E(XK), where k > -4. Enter a formula below. Use * for multiplication, / for divison, ^ for power, lam for 1, Gamma for the function, and pi for the mathematical constant i. For example, lam^k*Gamma(k/2)/pi means ik r(k/2)/n. Hint 1: Consider u = 1x2 or u = x2....
Let > 0 and let X1, X2, ..., Xn be a random sample from the distribution with the probability density function f(x; 1) = 212x3e-dız?, x > 0. a. Find E(X), where k > -4. Enter a formula below. Use * for multiplication, / for divison, ^ for power, lam for \, Gamma for the function, and pi for the mathematical constant 11. For example, lam^k*Gamma(k/2)/pi means ik r(k/2)/ I. Hint 1: Consider u = 1x2 or u = x2....
across Let F = (x i+yj +z k'). What is the outward flux of F (x2 + y2 +22)8 a sphere of radius R> 0 centered at the origin?
1 xe Let f(x)={? x 8. Prove that f(x) continuous only at +1. Let f(x)= $3.x xs! x >1 Using the definition prove lim f(x)=1 and lim f (x) = 3 x>17 11°
Let X1, X2, Xn be a random sample from the distribution with probability density function > - 7+tx 7 f(x; t) 0 x 2 2 14+2t a. Find the method of moments estimator of t, t. Enter a formula below. Use * for multiplication, / for division and A for power. Use m1 for the sample mean X. For example, 7*n^2*m1/6 means 7n2X/6. b. Suppose n-5, and x1-0.60, x2 0.95, x3=1.06, x4 1.18, x5-1.52. Find the method of moments estimate...
7 7. Let Xi, . . . , xn be iid based on f(x:0) = 2x e-x2/0 where x > 0, Show that θ =「X 2 is 2-1 efficient.
Please help me to solve this probability problem. 2. Consider a random variable X with the following PDF f(x) f(x) = for 0s x<1 x, 2-x for 1s XS2 otherwise (a) Consider 6 independent random variables X, X2, X3, X4, X5, Xs with the PDF f(x) given above. What will be the PDF of Y= (X1+X2+ X3+ X4+ Xs* X6) approximately? Explain it. (b) Compute the probability of Y>8.
Are the following functions concave, convex, or neither for x > 0? (i) f(z) =ztt convex, (i) f (x)x -2 (iii) f (x) = x In x (iv) f (x)-/Inr (v) f (x) = min(x2, x3}