Question

(Problem 6)     In a popular day care center, the probability that a child will play with the computer is 0.45; the probability that he or she will play dress-up is 0.27; play with blocks, 0.18; and paint, 0.1. a) Construct the probability distribution for this discrete random variable.

b)         What is the Probability a child plays with a computer or paint

(Problem 7)     The county highway department recorded the following probabilities for the number of accidents per day on a certain freeway for one month. The number of accidents per day and their corresponding probabilities are shown. Find the mean, variance, and standard deviation.

Can you make sure I answered it correctly

Given:

Number of accidents X	0	1	2	3	4
Probability P(X )	0.4	0.2	0.2	0.1	0.1
my answer

x	p(x)	x*p(x)	X^2 *P(x)
0	0.4	0	0
1	0.2	0.2	0.008
2	0.2	0.4	0.016
3	0.1	0.3	0.003
4	0.1	0.4	0.004
total	1	1.3	0.031

Mean: 1.3

Variance= -1.66

SD= 1.29

Answer 1

Problem 6:

(a)

Probability Distribution for the Discrete Random Varable:

Let:
x = 1 for computer

      2 for dress - up

     3 for blocks

     4 for paint

Thus, we get tehe Discrete Probability Distribution as follows:

x	p(x)
1	0.45
2	0.27
3	0.18
4	0.10

(b)

P(Computer OR Paint) = P(x = 1 OR 4) = (x= 1) + P(x=4) = 0.45+ 0.10 = 0.55

Problem 7:

x	p	xp	x2 p
0	0.4	0	0
1	0.2	0.2	0.2
2	0.2	0.4	0.8
3	0.1	0.3	0.9
4	0.1	0.4	1.6

Total                                              1.3                          3.5

Mean = E(x) = 1.3

E(X²) = 3.5

Variance = E(X²) - (E(X))²

            = 3.5 - 1.3² = 1.81

Standard Deviation = = 1.3454