1. Suppose X is a continuous random variable. Find an example of a probability density function for X giving expected value E(X) = 1 and variance V (X) = 3 if X has . . . (a.) a uniform distribution. (b.) an exponential distribution. (c.) a normal distribution. In each case, if there is no such probability density function, explain why this is so.

1. Suppose X is a continuous random variable. Find an example of a probability density function for X giving expected value E(X) = 1 and variance V (X) = 3 if X has . . . (a.) a uniform distribution. (b.) an exponential distribution. (c.) a normal distribution. In each case, if there is no such probability density function, explain why this is so.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Q. 2 Suppose I see students during regular office hours. Time spent with students follow an exponential distribution with mean of 20 minutes. (i) Write the probability density function of random variable X, E (X) and Var(X). (ii) Find the probability that a given student spends less than 0.4 hours with the professor. (iii) Find the probability that a given student spends between 0.20 and 0.5 hours with the professor. (iv) Find the probability that a given student spends at least 0.75 hours with the professor.
Suppose that a random variable X has the following probability density function. SC(36-x²) 0 ≤ x ≤ 6 otherwise f(x) = {C (² Find the expected value of X. (You will need to find the value of the constant C so that f is a pdf.)
Choose ALL THE CORRECT STATEMENTS in the following ones about probability distribution. i. Probability mass function indicates the probability distribution of a continuous random variable. ii. Probability mass function indicates the probability distribution of a discrete random variable. iii. The probability mass function of a discrete random variable X at a is denoted by P(X < a). iv. The probability function of a continuous random variable Y can be described by using P(Y= a).
Q.2 Let X has the following probability density function: fx(x) = a e-ax;x > 0 Find moment generating function and then using it find mean and variance. End of Quiz
Please answer this statistic question
7. If a random variable has the probability density function -1≤x≤3 otherwise f(x)=k(x²-1) =0
Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.
Please give answers of my questions that I have uploaded as an image.
Question 2: X ~ Geometric(T) distribution with probability function p(x) = P(X = x) = T(1 – 7)"-1 for x = 1, 2, 3, ... Find P(X x).