Tutorial 21. Suppose that a fair coin is tossed five times independently. Let V be the number of tailsobtained on the ten tossed. Determine the possible value of V.2. During the summer months, a rental agency keeps track of the number of speedboatsrented each day during a period of 90 days. The variable X represents the number ofa radomspeedboats rented per day. The results are shown as follow.12Number of days4530150.SD. 330,17Compute probability P(X) for each X3. Suppose that a box contained seven red balls and three blue balls. If four balls areselected at random without replacement, determine the probability distribution functionof the number of red balls that will be obtained.4. Determine whether each distribution is a probability distribution(a)101520P(X=x)111(b)13.4.P(X=x)16.Yes8.1616(c)P(X-x)0.50.30.4No2)1/42) (d)26.P(X=x)-1.01.50.30.2No5. The probability distribution of discrete random variable X is given by1213P(X = x)kfor x = 1, 2,3x +1(a) Find the value of k where k is a constant0,3077(b) Compute P(X = 2)(c) Compute P(X 2 or X = 3)0.53P5Tonoituat oi6. Let k be a constant and consider the probability distribution functionkx,x = 1,2,3P(X = x) = {k(6- x), x = 4,50,otherwiseFind the value of k.1lowin7.8. A shipment of seven television sets contains two defective sets. A hotel makes a randompurchase of three of the sets. If x is the number of defective sets purchased by the hotel,find012(a) the probability distribution of X.(b) the cumulative distribution of X.(c) P(X = 1))(d) P(1 < X < 2) P(x =2)

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Suppose that a fair coin is tossed five times independently. Let V be the number of tails obtained on the ten tossed. Determine the possible value of V.

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

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

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Tutorial 2
1. Suppose that a fair coin is tossed five times independently. Let V be the number of tails
obtained on the ten tossed. Determine the possible value of V.
2. During the summer months, a rental agency keeps track of the number of speedboats
rented each day during a period of 90 days. The variable X represents the number of
a radom
speedboats rented per day. The results are shown as follow.
1
2
Number of days
45
30
15
0.S
D. 33
0,17
Compute probability P(X) for each X
3. Suppose that a box contained seven red balls and three blue balls. If four balls are
selected at random without replacement, determine the probability distribution function
of the number of red balls that will be obtained.
4. Determine whether each distribution is a probability distribution
(a)
10
15
20
P(X=x)
1
1
1
(b)
1
3.
4.
P(X=x)
1
6.
Yes
8.
16
16
(c)
P(X-x)
0.5
0.3
0.4
No
2)
1/4
2)

(d)
2
6.
P(X=x)
-1.0
1.5
0.3
0.2
No
5. The probability distribution of discrete random variable X is given by
12
13
P(X = x)
k
for x = 1, 2,3
x +1
(a) Find the value of k where k is a constant
0,3077
(b) Compute P(X = 2)
(c) Compute P(X 2 or X = 3)
0.53P5
Tonoituat oi
6. Let k be a constant and consider the probability distribution function
kx,
x = 1,2,3
P(X = x) = {k(6- x), x = 4,5
0,
otherwise
Find the value of k.
1lowin
7.
8. A shipment of seven television sets contains two defective sets. A hotel makes a random
purchase of three of the sets. If x is the number of defective sets purchased by the hotel,
find
012
(a) the probability distribution of X.
(b) the cumulative distribution of X.
(c) P(X = 1))
(d) P(1 < X < 2) P(x =2)

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