13. Let X be the number of heads in two tosses of a coin.(a) Find the probability distribution function of X. 4,I.7(b) Find the expected value of X.E(x) = Ex P(x)0,1,214. The probability distribution of the discrete random variable X is3-xP(X = x) = )) G),x = 0,1,2,3Find the mean and variance of X.15. The probability that 0, 1, 2, 3 or 4 people will be placed on hold when they call a radiotalk show is shown in the distribution13.4P(X=x)0.180.340.230.210.04Find the variance and standard deviation for the data. to to9. For the following probability distribution in Exercise 4(b), find each of the followingprobabilities:(a) P(X 2 2)(b) P(X < 4) s(c) P(1 < X < 4) 16fo at(d) P(2 < X < 4)10. A box has seven items, four good and three defective. Three items are selected at randomwithout replacement. Let X be the number of good items.(a) Find the probability distribution function of X(b) Find the cumulative distribution function of X.(c) Suppose that we have loss of RM 20 for each defective item selected. Let the randomvariable Y denote the loss. Find the probability distribution function of Y.11. Let X denotes the number of busy server at the checkout counters in a hotel at 1 p.m. Theprobability distribution function of X is3.4p(x)0.20.30.30.10.1(a) Find the cumulative distribution function of X.0.1 0. S, 0.8,0.9.1.0(b) Find the probability that three or more servers are busyP(X 3)0.1 +0.1- 0.212. Let Z denotes a random variable with probability distribution function.-2-10.12.3.P(Z=z)0.10.3k0.090.050.250.21(a) What is k?. Đ.09(b) Find the cumulative distribution function of 7 0.1, 0.4, 0.49, 0. S4, 0.79,!(c) Find P(-1< X S 2), P(Z > 0), P(Z < 2)and P(-2

Answered: Image /qna-images/answer/c3df326f-152d-4301-8161-8f638134b4bd.jpg

Answered: 13. Let X be the number of heads in two…

13. Let X be the number of heads in two tosses of a coin. (a) Find the probability distribution function of X. .T (b) Find the expected value of X. E(x) = Ex P(x) 0,1,2

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

13. Let X be the number of heads in two tosses of a coin.
(a) Find the probability distribution function of X. 4,I.7
(b) Find the expected value of X.
E(x) = Ex P(x)
0,1,2
14. The probability distribution of the discrete random variable X is
3-x
P(X = x) = )) G)
,x = 0,1,2,3
Find the mean and variance of X.
15. The probability that 0, 1, 2, 3 or 4 people will be placed on hold when they call a radio
talk show is shown in the distribution
1
3.
4
P(X=x)
0.18
0.34
0.23
0.21
0.04
Find the variance and standard deviation for the data.

to to
9. For the following probability distribution in Exercise 4(b), find each of the following
probabilities:
(a) P(X 2 2)
(b) P(X < 4) s
(c) P(1 < X < 4) 16
fo at
(d) P(2 < X < 4)
10. A box has seven items, four good and three defective. Three items are selected at random
without replacement. Let X be the number of good items.
(a) Find the probability distribution function of X
(b) Find the cumulative distribution function of X.
(c) Suppose that we have loss of RM 20 for each defective item selected. Let the random
variable Y denote the loss. Find the probability distribution function of Y.
11. Let X denotes the number of busy server at the checkout counters in a hotel at 1 p.m. The
probability distribution function of X is
3.
4
p(x)
0.2
0.3
0.3
0.1
0.1
(a) Find the cumulative distribution function of X.
0.1 0. S, 0.8,0.9.1.0
(b) Find the probability that three or more servers are busy
P(X 3)
0.1 +0.1
- 0.2
12. Let Z denotes a random variable with probability distribution function.
-2
-1
0.
1
2.
3.
P(Z=z)
0.1
0.3
k
0.09
0.05
0.25
0.21
(a) What is k?. Đ.09
(b) Find the cumulative distribution function of 7 0.1, 0.4, 0.49, 0. S4, 0.79,!
(c) Find P(-1< X S 2), P(Z > 0), P(Z < 2)and P(-2 <Z < 2)
= 0.79
= 0.69
E 0.51
:0,79

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