Concept explainers
Let
Using the pdf of Y. we find that
Use the central limit theorem to approximate this probability.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Probability And Statistical Inference (10th Edition)
- Suppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)arrow_forwardFor a random variable (X) having pdf given by: f(x) = (k)x^3 where 0 ≤ x ≤ 1, compute the following: a) k b) E(X). c) Var(X). d) P(X > 0.25).arrow_forwardIf X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?arrow_forward
- Suppose that X and Y have a joint probability density function f(x,y)= 1, if0<y<1,y<x<2y; 0, otherwise. (a) Compute P(X + Y less than or equal 1). (b) Find the marginal probability density functions for X and Y , respectively. (c) Are X and Y independent?arrow_forwardLet X denote the voltage at the output of a microphone, and suppose that X has a uniform distribution on the interval from −1 to 1. The voltage is processed by a "hard limiter" with cutoff values −0.5 and 0.5, so the limiter output is a random variable Y related to X by Y = X if |X| ≤ 0.5, Y = 0.5 if X > 0.5, and Y = −0.5 if X < −0.5. (a) What is P(Y = 0.5)? (b) Obtain the cumulative distribution function of Y. Please show your work, thanks!arrow_forward
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON