3. Given a discrete random variable X with probability mass function (pmf)fx(x) = {"(*- 6), for x = 7,8,90,otherwise3.1 Solve for k.3.2 Give the expected value of X, µx.3.3 Give the standard deviation of X, ox.3.4 Give the cumulative distribution function (caf) of X, F, (x).3.5 Give the following probabilities:3.6 Give the moment generating function of X, mx(t).(a) Fx(8.3) = P[X < 8.3](b) fx(8.3) = P[X = 8.3]

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Answered: 3. Given a discrete random variable X…

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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Areas under normal distribution curves can be used calculate probabilities of many random variables in the natural and social sciences. The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below, and its function is given by 1 f(x) = √2T e 1 The integral of e dx would be used to calculate the probability of an event that occurs √2T -1.5 between -1.5 to 1.5 standard deviations from the mean. (-1.5, 0.13) 1 Unfortunately, √2π -1.5 methods to approximate the values. 1.5 -1.5 1.5 (-1, 0.24) Using Simpson's Rule, (-0.5, 0.35) e dx has no proper closed form antiderivative, so we must use numerical 1.5 -1.5 1-0.5 -0-2 Using the Midpoint Rule with three rectangles of equal width, dx 0 Using the Trapezoidal Rule with six trapezoids of equal width, (0, 0.4) 0.5 Round answers to 4 decimal places when appropriate. (0.5, 0.35) (1, 0.24) 1.5 Ibe 1.5 1.5 [ 13 e-t de = \ е 1.5 e-2 е dx (1.5, 0.13)
Solve number 2 only
4. Question 4: Y is a discrete random variable with PMF S1/3, y=1 p(y) = 2/3, y = 2 (a) Find the MGF for Y. (b) Develop the first two raw moments from MGF and find the variance V(Y). Answers:
9. Zero-mean Gaussian random variables x and y have variance oz= 3 and o= 4 respectively and a y -1 correlation coefficient p = ing Write an expression for the joint density function.
1. A random variable X has the following probability mass function. Pr(X = x) 1 2. 1 24 1 Calculate E(X), Var(X) and standard deviation of X.
Bapu
X 1:YY KB/S robability & Statistics Time left 1:12:20 For the probability distribution in the table. What is the probability of 1 or 5 P(x) 1 0. 2 2 0. 15 3 0.1 4 0. 15 5 a. 0. 52 b. Correct answer is not listed с. .4 d. 0. 08 е. О. 6
Question 1.2 Consider the function f (x) = (1/24(x^2 +1) 1 < or = x < or = 4) = (0 otherwise) Calculate P (x = 3) Calculate P (2 < or = x < or = 3) Question 1.3 Consider the function f (x) = (k - x/4 1 < or = x < or = 3) = (0 otherwise) which is being used as a probability density function for a continuous random variable x? a. Find the value of K b. Find P (x < or = 2.5)
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b) The probability density function of random variable X is given as: - Вх {*5 if 0 < x < 1 otherwise f(x) = If the expected value of the random variable X is 1/3. Find the values A and B.
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).
5

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3. Given a discrete random variable X with probability mass function (pmf) fx (x) = {"C Sk(x -6), for x = 7, 8,9 0, otherwise 3.1 Solve for k. 3.2 Give the expected value of X, µx. 3.3 Give the standard deviation of X, ox.