3. (25 P) Account balance of customers in a bank have the following probability density function:...
3. (25 P) Account balance of customers in a bank have the following probability density function: f(x) = 0.05, a, 0, 0 < x <5 5 sx < 10 otherwise a. Develop a random variate generator for the distribution b. Generate 3 values of the random variate using R 1 = 0.1, R2 = 0.2, R 3 = 0.95.
1 3. (25 P) Account balance of customers in a bank have the following probability density function: 2 3 (0.05, 0<x< 5 4 f(x) = a, 5 <x< 10 5 0, otherwise 6 7 a. Develop a random variate generator for the distribution 8 9 b. Generate 3 values of the random variate using R 1 = 0.1. R 2 = 0.2. R 3 = 0.95. 10 11 12 13 14 15 16 17 18 19 20 21 22 23
1 3. (25 P) Account balance of customers in a bank have the following probability density function: 2 3 (0.05, 0<x< 5 4 f(x) = a, 5 <x< 10 5 0, otherwise 6 7 a. Develop a random variate generator for the distribution 8 9 b. Generate 3 values of the random variate using R 1 = 0.1. R 2 = 0.2. R 3 = 0.95. 10 11 12 13 14 15 16 17 18 19 20 21 22 23
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
2.6.17. The probability density function of the random variable X is given by r2 21 0<x-1, 6x-2r2-3 (x, 3)2 0 otherwise.
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)
3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...
Question 2 (30 pts) Suppose that X is a continuous random variable with the following probability density function: 2 /(x) = (2 _-), for 3 < x 6 0, otherwise Develop a random-variate generator for the random variable X by using the inverse-transform technique.
Let random variable X follows an exponential distribution with probability density function fx (2) = 0.5 exp(-x/2), x > 0. Suppose that {X1, ..., X81} is i.i.d random sample from distribution of X. Approximate the probability of P(X1+...+X81 > 170). A. 0.67 B. 0.16 C. 0.33 D. 0.95 E. none of the preceding
2.6.17. The probability density function of the random variable X is given by 6x-21-3 -, 2<x<3 0, otherwise. Find the expected value of the random variable X.