The lifetime of a physical mechanism is given as f(x) = {(c/x^2 if 1< x < infinity; 0 otherwise)}
a. Determine the value of the constant c that makes f a probability density function.
b. Compute P(1< X < 2)
The lifetime of a physical mechanism is given as f(x) = {(c/x^2 if 1< x <...
Let X be the lifetime of a certain type of electronic device (measured in hours). The probability density function of X is f(x) =10/x^2 , x > c 0, x ≤ c (a) Find the value of c that makes f(x) a legitimate pdf of X. (b) Compute P(X < 20).
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2). (c) Let W=X/Y. Compute the density function of W. (d) Are X and Y independent? Justify briefly.
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find 2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2). (c) Let W=X/Y. Compute the density function of W. (d) Are X and Y independent? Justify briefly.
5. Let the joint probability density function of X and Y be given by, f(x,y) = 0 otherwise (a) Find the value of A that makes f (x, y) a proper probability density function (b) Calculate the correlation coefficient of X and Y. (c) Are X and Y independent? Why or why not?
2. For a laboratory assignment, suppose that the measurement error X of a certain physical quality is determined by the density function1 - { k(x+1) 0 < x < 10 otherwise fx (x) 0 (a) Determine k that renders f(x) a valid density function. (b) What is the probability that X is more than 2.5? (c) What is the probability that X is between 1 and 3? (d) Find the expected value of X
4. The random variable X has probability density function f(x) given by f(x) = { k(2- T L k(2 - x) if 0 sxs 2 0 otherwise Determine i. the value of k. ii. P(0.7 sX s 1.2) iii. the 90th percentile of X.
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).