Let X be a random variable with the following probability distribution.Value x of X P(X=x)0.051*0.5020.203.0.200.05Complete the following. (If necessary, consult a list of formulas.)(a) Find the expectation E(X) of X.E(X) - ||(b) Find the variance Var(X) of XVar (x) = []Checkacer->esc%23%246.!@421retabf

Given: Let X be a random variable .

Answered: Let X be a random variable with the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In the following probability distribution, X represents the number of calls a telemarketer makes in a day, and the probability they make that many calls. П. 75 0.05 X 100 50 0.01 125 150 175 P(X) 0.15 0.20 0.30 a) Find P(X=175) b) Find E[X] ( c) Find the Variance and Standard Deviation ofX
Exercise(3): If the mean and variance of a binomial distribution are 9 and 6 respectively, then find: (1) The probability mass function P(x = k) (2) P(x=3) (3) P(x>1)
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. + Part (a) O Part (b) Part (c) Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization. Write the probability statement. P(X > x) = |0.98
Losses come from a mixture of an exponential distribution with mean 100 with probability p and an exponential distribution with mean 10,000 with probability 1– p. Losses of 100 and 2000 are observed. Determine the likelihood function of p. -0.01 pe (1– p)e“ pe 20 (1– p)e0² -0.2 (A) 100 10,000 100 10,000 pe (1– p)e“ -0.01 (B) pe (1– p)e02' 100 10,000 100 10,000 pe, (1- p)e0. 20 (1– p)eº -0.01 pe 100 -0.2 (C) pe 10,000 100 10,000 pe, (1- p)e 00i -0.01 (D) -20 ре (1– p)e02 100 10,000 100 10,000 e 0.01 +(1– p) e -20 (E) р. 100 10,000 100 10,000
Q1. 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.
Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. n=51 p=.03 x=20

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Let X be a random variable with the following probability distribution. Value x of X P(X=x) 0.05 0.50 0.20 0.20 0.05 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E(X ) of X. E(X)-] 5 ? (b) Find the variance Var(X) of X. Var (x) = []