Question

Three tables listed below show random variables and their probabilities. However, only one of these is actually a probability distribution.

A			B			C
X	P(X)		X	P(X)		X	P(X)
5	0.3		5	0.1		5	0.5
10	0.3		10	0.2		10	0.3
15	0.2		15	0.3		15	−0.2
20	0.4		20	0.4		20	0.4

b. Using the correct probability distribution, find the probability that x is: (Round the final answers to 1 decimal place.)

1.	Exactly 15 =
2.	No more than 10 =
3.	More than 5 =

c. Compute the mean, variance, and standard deviation of this distribution.

1.	Mean µ
2.	Variance σ2
3.	Standard deviation σ

Answer 1

A distribution is said to be probability distribution if-

1) P( x 0)

2) Sum of all probabilities = 1 that is P(x) = 1

In B we get all probabilities greater than 0 and sum of all probabilities equal to 1.

Hence table B is the probability distribution.

b)

1. P(x = 15) = 0.3

P(Exactly 15) = 0.3

2. P(no more than 10 ) = P( x = 5) + P(x = 10)

= 0.1 + 0.2

= 0.3

P(no more than 10 ) = 0.3

3. P( more than 5) = P(x = 10 ) + P(x = 15) +P(x = 20)

= 0.2 + 0.3 +0.4

= 0.9

P( more than 5) = 0.9

c)

1) Mean = n * p =15

2) variance ² = (x - mean)²*P(x) = 25

3) Standard deviation = = 5

Hope this will help you. Thank you :)