Suppose both X and Y are independent and distributed according to Geo(0.2). Compute P(min{X,Y} < 4).
Suppose both X and Y are independent and distributed according to Geo(0.2). Compute P(min{X,Y} < 4).
Suppose both X and Y are independent and distributed according to Geo(0.2). Compute P(min{X,Y} < 4). Hint: If X ~Geo(p), then FX(k) = 1 -(1 -p)k.
Supposed both X and Y are independent and distributed according to Geo(0.2). Compute P(min {X,Y} < 4). Hint: if x tilda Geo(P), then Fx (k) = 1 - (1 - p)^k.
o Additional Problem 3: Suppose both X and Y are independent and distributed according to Geo(0.2). Compute P(min (X, Y Hint: If X ~ Geo(p), then FX (k) = 1-(1-pt. < 4).
9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Y|Y -1 0 1 0.1 0.1 0.1 3 0 0.2 0.1 4. 0.2 0.1 0.1 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]
-1 1 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: 0 0.1 0.1 0.1 3 0 0.2 0.1 4 0.2 0.1 0.1 2x 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Yl-1 0 1 0.1 0.1 0.1 0 0.2 0.1 0.2 0.1 0.1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. (11) b. Let W = X - Y. Compute E(W) and V(W). [4] 10. Let X be a continuous random variable with probability density function h(x) ce* r >...
Suppose that X and Y are independent, identically distributed, geometric random variables with parameter p. Show that P(X = i|X + Y = n) = 1/(n-1) , for i = 1,2,...,n-1
Let random variable X be distributed according to the p.m.f P(a) 0.3 0.5 0.2 · If Y = 2x, what are ELY Var(Y) If Z = aX + b has E121 = 0 and Var(Z) = 1, what are: .
Let random variable X be distributed according to the p.m.f P( 0.3 0.5 0.2 · If Y=2X, what are li E r Var(Y) . If Z = aX + b has EZj-0 and Var(Z)-1, what are: lal
Problem 4. Let X and Y be independent Geom(p) random variables. Let V - min(X, Y) and Find the joint mass function of (V, W) and show that V and W are independent