FIRST COURSE IN PROBABILITY (LOOSELEAF)
10th Edition
ISBN: 9780134753751
Author: Ross
Publisher: PEARSON
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Chapter 1, Problem 1.1P
a. How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers?
b. Repeat part (a) under the assumption that no letter or number can be repeated in a single license plate.
(a)
Expert Solution
To determine
The number of different 7-place license plates.
Answer to Problem 1.1P
67600000
Explanation of Solution
Given:
First 2 places are for letters.
Other 5 places are for numbers.
Calculation:
Total number of letters is 26 (A to Z)
Total number of digits is 10 (0 to 9)
Applying the basic principle of counting, number of license plates will be
(b)
Expert Solution
To determine
The number of different 7-place license plates.
Answer to Problem 1.1P
19656000
Explanation of Solution
Given:
First 2 places are for letters.
Other 5 places are for numbers.
No letter or number can be repeated in a single license plate.
Calculation:
As there can be no repetition,
The first place letter has 26 options.
The second place letter has 25 options.
The third place digit has 10 options.
The fourth place digit has 9 options.
The fifth place digit has 8 options.
The sixth place digit has 7 options.
The seventh place digit has 6 options.
Applying the basic principle of counting, number of license plates will be
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Students have asked these similar questions
QUESTION 18 - 1 POINT
Jessie is playing a dice game and bets $9 on her first roll. If a 10, 7, or 4 is rolled, she wins $9. This happens with a probability of . If an 8 or 2 is rolled, she loses her $9. This has a probability of J. If any other number is rolled, she does not win or lose, and the game continues. Find the expected value for Jessie on her first roll.
Round to the nearest cent if necessary. Do not round until the final calculation.
Provide your answer below:
5 of 5
(i) Let a discrete sample space be given by
Ω = {ω1, 2, 3, 4},
Total marks 12
and let a probability measure P on be given by
P(w1) 0.2, P(w2) = 0.2, P(w3) = 0.5, P(w4) = 0.1.
=
Consider the random variables X1, X2 → R defined by
X₁(w3) = 1, X₁(4) = 1,
X₁(w₁) = 1, X₁(w2) = 2,
X2(w1) = 2, X2(w2) = 2, X2(W3) = 1, X2(w4) = 2.
Find the joint distribution of X1, X2.
(ii)
[4 Marks]
Let Y, Z be random variables on a probability space (N, F, P).
Let the random vector (Y, Z) take on values in the set [0,1] × [0,2] and let the
joint distribution of Y, Z on [0,1] × [0,2] be given by
1
dPy,z(y, z)
(y²z + y²²) dy dz.
Find the distribution Py of the random variable Y.
[8 Marks]
Total marks 16
5.
Let (,,P) be a probability space and let X : → R be a random
variable whose probability density function is given by f(x) = }}|x|e¯|×| for
x Є R.
(i)
(ii)
Find the characteristic function of the random variable X.
[8 Marks]
Using the result of (i), calculate the first two moments of the
random variable X, i.e., E(X") for n = 1, 2.
(iii) What is the variance of X?
[6 Marks]
[2 Marks]
Chapter 1 Solutions
FIRST COURSE IN PROBABILITY (LOOSELEAF)
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