(2] 5-81)Suppose that X is a continuous random variable with probability distribution a) Determine the probability...
Suppose that X is a continuous random variable with probability distribution Suppose that X is a continuous random variable with probability distribution O<x<6 18 (a) Find the probability distribution of the random variable Y-10X 3. fr o) 2 Edit for Sy s (b) Find the expected value of Y
Suppose that X is a continuous random variable with probability distribution fx (x) = 0x6 18 (a) Find the probability distribution of the random variable Y = 15X10 fr (y) Edit ys for (b) Find the expected value of Y
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with parameters α = 0.4 and xo = 0.45, ie, ;x 2 0.45 x 〈 0.45 f(x) = (2.5e-2.5 (-0.45) Variable Y is a function of X: a) Find the first order approximation for the expected value and variance of Y b) Find the probability density function (PDF) of Y. c) Find the expected value and variance of Y from its PDF Problem 5. Let X...
I think it is x/18 Suppose that X is a continuous random variable with probability distribution fX(x) = x 18, Osxs6 (a) Find the probability distribution of the random variable Y = 19X+11. fY(y) = ? Edit
7. Let X be a continuous random variable with probability density function: 0, 5+2x if if 0 if x> 10 x<b f(x)=re, 76-0 5310 x 10 150 o Find the expected value and mode of random variable X. Part 3. Statistics The following sample is given 3.15 3.25 3.25 3.35 3.45 3.5 3.5
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
2ND TEST IN PROBABILITY THEORY AND STATISTICS Variant 8 1. X is a continuous random variable with the cumulative distribution function if x<0 F(x)ax2 0.1x if osxs 20 if x> 20 0 Find 1) the coefficient a; 2) P 10); 3) P(X<30). 2. The result of some measurement X is normally distributed with parameters 184 and 8. Compute the probability that variable X takes value from interval (170;180) at least once in 5 experiments 3. Two independent random variables X...
Suppose that X is continuous random variable with 2. 1 € [0, 1] probability density function fx(2) = . Compute the 10 ¢ [0, 1]" following: (a) The expectation E[X]. (b) The variance Var[X]. (c) The cumulative distribution function Fx.
Suppose hat the joint probability distribution of the continuous random variables X and Y is constant on the rectangle 0 < x < a and 0 < y < b for a, b E R+. Show mathematically that X and Y are independent. Hint: (a) Recall JDx "lly f(r, y) dy dx-1 (b) Recall X, Y are independent if ffy fry Suppose hat the joint probability distribution of the continuous random variables X and Y is constant on the rectangle...
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.