6. (10 points) Suppose X – Exp(1) and Y = -In(X) (a) Find the cumulative distribution...

Question

Question

6. (10 points) Suppose X – Exp(1) and Y = -In(X) (a) Find the cumulative distribution function of Y. (b) Find the probability

(c) Let X1, X2,...,be i.i.d. Exp(1), and let Mk = max(X1,..., Xk) (Maximum of X1, ..., Xk). Find the probability density func

Answer 1

Answer #1

given that XnEXP (1), 4 =-10 (x) a) cumulative distribution function of y. b) Find the proljability density fun of 4 a) cumul

Answer 2

Similar Homework Help Questions

Suppose X = Exp(1) and Y= -ln(x) (a)Find the cumulative distribution function of Y . (b)...

Suppose X = Exp(1) and Y= -ln(x) (a)Find the cumulative distribution function of Y . (b) Find the probability density function of Y . (c) Let X1, X2, ... , Xk be i.i.d. Exp(1), and let Mk = max{X1,..... , Xk)(Maximum of X1, ..., Xk). Find the probability density function of Mk.(Hint: P(min(X1, X2, X3) > k) = P(X1 >= k, X2 >= k, X3 >= kq, how about max ?) (d) Show that as k → 00, the CDF...
6. (10 points) Suppose X ~ Exp(1) and Y = -ln(X) (a) Find the cumulative distribution...

6. (10 points) Suppose X ~ Exp(1) and Y = -ln(X) (a) Find the cumulative distribution function of Y. (b) Find the probability density function of Y.
Suppose X1, X2, Xz~exp(1) and they are independent. (a) Compute the cdf of X1 (b) Let...

Suppose X1, X2, Xz~exp(1) and they are independent. (a) Compute the cdf of X1 (b) Let Y- max(Xi, X2, X3). Find the cdf of Y (c) Derive the pdf of Y

4. Suppose Xi, X2, X3 ~exp(1) and they are independent (a) Compute the edf of X...

4. Suppose Xi, X2, X3 ~exp(1) and they are independent (a) Compute the edf of X (b) Let Y max(Xi, X2, X3). Find the cdf of Y. (c) Derive the pdf of Y
(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution functio...

(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution function and the density function of U and of V (b) Show that the joint density function of U and V is fe,y(u, u)= n(n-1)/(u)/(v)[F(v)-F(u)]n-1, ifu < u. (7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi...
Let X1, X2, X3,…Xn is a random sample, where X~Exp(1/θ) and U=2Y/θ. a) Find the cumulative...

Let X1, X2, X3,…Xn is a random sample, where X~Exp(1/θ) and U=2Y/θ. a) Find the cumulative distribution function of U. (8pts) b) Is U a pivot (2pts) c) Find the 95% CI for θ.(10pts)

7. Suppose that Xi,..., Xk are independent random variables, and X, ~ Exp(B) for i =...

7. Suppose that Xi,..., Xk are independent random variables, and X, ~ Exp(B) for i = 1, . . . , k. Let Y = min(X1 , . . . , Xk). Show that Y ~ Exp(Σ-1 β).
4a). Let X1 and X2 be independent random variables with a common cumulative distribution function...

4a). Let X1 and X2 be independent random variables with a common cumulative distribution function (i.e., c.d.f.) F(y) = { 0" if0cyotherwise。 Find the p.d. f. of X(2,-max(X, , xa). Are X(1)/X(2) and X(2) independent, where X(1,-min(X,, X2) ? 4a). Let X1 and X2 be independent random variables with a common cumulative distribution function (i.e., c.d.f.) F(y) = { 0" if0cyotherwise。 Find the p.d. f. of X(2,-max(X, , xa). Are X(1)/X(2) and X(2) independent, where X(1,-min(X,, X2) ?
Let f(x,y) = exp(-x) be a probability density function over the plane. Find the probabilities: Parta)P(...

Let f(x,y) = exp(-x) be a probability density function over the plane. Find the probabilities: Parta)P( X2 + y2 <a), a > 0, Part b)P(x2 + y2 <a), a > 0.

2. Suppose that (X,Y) has the following joint probability density function: f(x,y) = C if -1...

2. Suppose that (X,Y) has the following joint probability density function: f(x,y) = C if -1 <r< 1 and -1 <y<1, and 0 otherwise. Here is a constant. (a) Determine the value of C. (b) Are X and Y independent? (Explain why or why not.) (c) Calculate the probability that 2X - Y > 0 (d) Calculate the probability that |X+Y| < 2 3. Suppose that X1 and X2 are independent and each is standard uniform on (0,1]. Let Y...