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Three tables listed at the top of page 190 show “random
Chapter 6, Problem 3E(choose chapter or problem)
Problem 3E
Three tables listed at the top of page 190 show “random variables” and their “probabilities.” However, only one of these is actually a probability distribution.
a. Which is it?
x |
P(x) |
5 |
.3 |
10 |
.3 |
15 |
.2 |
20 |
.4 |
X |
P(x) |
5 |
.1 |
10 |
.3 |
15 |
.2 |
20 |
.4 |
X |
P(x) |
5 |
.5 |
10 |
.3 |
15 |
−.2 |
20 |
.4 |
b. Using the correct probability distribution, find the probability that x is: (1) Exactly 15. (2) No more than 10. (3) More than 5.
c. Compute the mean, variance, and standard deviation of this distribution.
Questions & Answers
QUESTION:
Problem 3E
Three tables listed at the top of page 190 show “random variables” and their “probabilities.” However, only one of these is actually a probability distribution.
a. Which is it?
x |
P(x) |
5 |
.3 |
10 |
.3 |
15 |
.2 |
20 |
.4 |
X |
P(x) |
5 |
.1 |
10 |
.3 |
15 |
.2 |
20 |
.4 |
X |
P(x) |
5 |
.5 |
10 |
.3 |
15 |
−.2 |
20 |
.4 |
b. Using the correct probability distribution, find the probability that x is: (1) Exactly 15. (2) No more than 10. (3) More than 5.
c. Compute the mean, variance, and standard deviation of this distribution.
ANSWER:
Solution :
Step 1 of 3:
Given the 3 tables.
Then the tables is given below.
x |
P(x) |
5 |
0.3 |
10 |
0.3 |
15 |
0.2 |
20 |
0.4 |
X |
P(x) |
5 |
0.1 |
10 |
0.3 |
15 |
0.2 |
20 |
0.4 |
X |
P(x) |
5 |
0.5 |
10 |
0.3 |
15 |
−0.2 |
20 |
0.4 |
Our goal is:
a). We need to find the probability distribution.
b). We need to find the probability of exactly 15, no more than 10, and more than 5.
c). We need to find the mean, variance, and standard deviation of this distribution.
a). Now we have to find the probability distribution.
x |
P(x) |
5 |
0.3 |
10 |
0.3 |
15 |
0.2 |
20 |
0.4 |
The above table sum is
Sum of P(x) = 0.3 + 0.3 + 0.2 + 0.4 = 1.2
X |
P(x) |
5 |
0.1 |
10 |
0.3 |
15 |
0.2 |
20 |
0.4 |
The above table sum is
Sum of P(x) = 0.1 + 0.3 + 0.2 + 0.4 = 1
X |
P(x) |
5 |
0.5 |
10 |
0.3 |
15 |
−0.2 |
20 |
0.4 |
The above table sum is
Sum of P(x) = 0.5 + 0.3 -0.2 + 0.4 = 1
The sum of probabilities of a distribution is always equals to 1.
Hence, second and third is actually a probability distribution.