3. For a multinomial distribution with; n-55, k-4, pi-0.1,p2-0.3, pj-0.4 and P4-0.2 find: P( У-10.y2-10.у,-20, y,-15)
Consider the probability distribution shown below: X 10 12 18 20 p(x) 0.2 0.3 0.1 0.4 Find the standard deviation of X.
3) Recall the Hardy-Weinberg problem described in your text (page 273-274). The multinomial distribution for random variables Yı, Y2, Y3 (can extend to more than 3) is given by n! P(Yı y1, Y2 = y2, Y3 = ya) Ул!ур!у! Рі Р2 р. where y + y3 = n and the parameters pi,P2, P3 are subject to the constraint p1 +p2 +p3 = 1. This distribution is an extension of the binomial distribution. In fact, the distribution of each Y, i=...
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
1. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random variable Z-0.5Y+x END TEST IN PROBABL ITY THEORY AND STAISTICS Variant 1 1. Two independent random vanables X and Y are given with their distribution laws: 2 0.7 0.1 P 0.2 0.3 0.5 0.2 Find 1) the variance of random varñable Y 2)...
Random variable X has a distribution: P(x=0)=0.2 ; P(x=1)=0.3 ; P(x=2)=0.1 & P(x=3)=0.3 ; P(x=4)=0.1. Find: a) E(x) and Var(x) b) Find Fx(Xo) c) Find quantile of order 1/4 and median d) Find P(2<=x<=4)
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer. (20 points) Consider the following joint distribution of X and...
Consider the following probability distribution: x P(x) 1 0.1 2 ? 3 0.2 4 0.3 What must be the value of P(2) if the distribution is valid? A. 0.6 B. 0.5 C. 0.4 D. 0.2 What is the mean of the probability distribution? A. 2.5 B. 2.7 C. 2.0 D. 2.9
Suppose Y has a hypergeometric distribution with N=20, n=4, and K=4. Find P(Y>2) and the mean of Y. Select one: a. 0.0134 and 0.4 b. 0.0134 and 0.8 c. 0.0134 and 0.536 d. 0.9866 and 0.8 e. None of others.
Consider the following discrete probability distribution: X -0.99 0.48 0.71 1.4 P(X) 0.1 0.4 0.3 0.2 a) What is E[X]? Round your answer to at least 3 decimal places. b) What is Var[X]? Round your answer to at least 3 decimal places.
15 Let X and Y have a trinomial distribution with n = 8, P1 = 0.4 and P2 = 0.1 f (x,y) = 8! 10.4*0.190.58---8,0 < x + y < 8,2 € N, Y EN x!y! (8 - x - y)! (a) Find E (Y|X = x), Var (Y|X = x) (b) Compute E (XY)