1. a.

x
0
1
2
P(X = x)
0.25
0.5
0.25

 

 

 

b.

2. The discrete random variable X has a probability distribution as follows:

x
3
4
5
6
7
P(X = x)
0.2
0.3
z
0.15
0.25

a. = 0.1

b. P(4 ≤ X ≤ 6) = 0.55

c. P(X < 5) = 0.5

d.

3.

a. Let X = number of heads

x
0
1
2
3
P(X = x)
1 / 8
3 / 8
3 / 8

1 / 8

b. Let X = total score of two dice

x
2
3
4
5
6
7
8
9
10
11
12
P(X = x)
1 / 36
1 / 18
3 / 36

1 / 9

5 / 36
1 / 6
5 / 36
1 / 9
3 / 36
1 / 18
1 / 36

c. Let X = difference between numbers on dice

x
0
1
2
3
4
5
P(X = x)
1 / 6
5 / 18
2 / 9

1 / 6

1 / 9
1 / 18

 

4. k = 0.1

5.a. The probability of 1.1 has to be wrong as the highest probability possible is 1.

b. The correct value is 0.1 (The probabilities then add up to 1.)

 

6.

x
0
1
4
P(X = x)
0.2
0.4
0.4

 

7.

x
0
1
2
3
4
P(X = x)
81 / 625
216 / 625
216 / 625
96 / 625

16 / 625

8. k = 1 / 15