Answered: X is a Gaussian random variable with…

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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There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2.a) Find the mean of this probability distribution. (i.e. Find E[X] )b) Find the variance and standard deviation of this probability distribution.(i.e. Find V[X] and SD[X])The random variables M and W are defined as follows:M = X+5 and W = (1/2)X+5c) Find E[M] and E[W].d) Find V[M] and V[W].e) Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.
a) A random variable has a binomial distribution. Findi) Its expexctation
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Q2) a). Two balanced dice are rolled. What is the probability that the sum of dots on the top space of both the dice is 10? b). The mean and standard deviation of a binomial probability distribution is 2 and I respectively. Calculate Probabilities for random variable X = 0, 1, 2, 3 and 4.
The finish of a hole depends on the edge of the bit used, only 1% of the holes with a new drill have an irregular cut, 3% have an irregular cut with average bits and 5% present irregular cut with worn bits. If 25% of the holes are made with new bits, 60% have average edges and 15% are worn out. [use 3 decimal places] a) If a piece is taken at random, what is the probability of having holes irregular? b) If a piece with irregular holes is taken, what is the probability that would have been made with an average drill bit?
Which one of the following is not a true for the Negative Binomial distribution ? a) The random variable can start at y =0 b) The trials in the experiment are independent c) The negative binomial distribution parameters are the number of successes and the probability of a success d) The random variable denotes the number of failures that occured until the rth success is obtained e) There are only two outcomes, a success and a failure
The items produced by a manufacturer have a probability equal to 0.3 of being defective. For a random sample of 10 items, the probability that at most 3 items are defective as given by R is 1-pbinom(3,10,0.3) pbinom (10,3,0.03) pbinom(3,10,0.3) dbinom(3,10,0.3)

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X is a Gaussian random variable with mean 3 and variance 9, determine the probability of the following events: a) X > 5, b) X < -3, c) |X| > 6