9. A random variable X has the following p.m.f: X0 1 2 3. P J0.1 0.3 0.4 0.2 And F(x) is the cdf for X, then F(2) = () (A) 0.2; (B) 0.4; (C)0.8 (D)I.
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- (2.d) We are interested in the function of X defined by Y = g(X) = X². What is CDF of Y in terms of CDF of X? (Note, in %3D the answer box SQRT=Square Root). Referring to Y = g(X) = XWhat is the expected value (2.e) of the function of the random variable, E[Y?6. Show that 1 s2 E1(Xi – x)² is unbiased estimator of the population variance o? i=1 п-1So 3 Let the random variable X shows the number of tires on a randomly selected automobile that are under inflated. The pmf of X is given by; P(x) 0.4 0.1 0.1 0.1 0.3 P(2 SXS 3)=? Oa 02 Ob 0.5 Oc 07 Od. 03 Oe 0.1
- 2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 11. A discrete random variable X follows the Uniform distribution if X takes values x = 1, 2, .., N, with P(X = x) = 1/N. Compute E(X), E(X²) and the variance Var(X). You may use the following identities: п(п + 1) (1) 2 п(п + 1)(2n + 1) (2) i=1Complete the following multiple choice questions. No work will be graded in the bonus problem. (a) E(X²)= 16. Compute E[-X(3X – 2)]. Assume that X is a random variable with E(X)= -3 and | (i) -54 (ii) -48 (iii) -33 (iv) -27Answer no. 1 onlyLet Y be a random variable with pdf f(y)=(3/64)y2(4-y), Osys4, zero elsewhere. Match the following. A. 0.31 B. 12.2 C. 16 D. 2.40 E. 0.64 select 1. E(Y)= select 2. V(Y)= select 3. Let X=3Y+5= E(X)= select 4. Let Z-5Y+3= V(Z)= select 5. P(YS2)34. Find the mean of the discrete random variable X with the following probability distribution. Use this formula. μ -ΣΙΧ . P (X)] P(x) х. Р(х) x2 x² . P(x) X 14 1 /½ 5. Referring to the table above, solve for the variance and standard deviation. Use this formula. o² = E[x2 . P(X)1 – µ? E[x² - P(X)] – µ² | O =