Answer:
Step-by-step explanation:
Since we know that for a distribution be a probability density function sum of all the probability events should be equal to 1 and all individual events should have probability between 0 and 1
a. x P(X=x)
0 -----3/8
1 -----1/4
2 -----3/8
P(X=0)+P(X=1)+P(X=2) = 3/8 + 1/4 + 3/8
P(X=0)+P(X=1)+P(X=2) = 6/8 + 2/8 = 1
This is a probability density function
b. x P(X=x)
0 ----0.2
1 ----0.1
2 ----0.35
3 ----0.17
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.2 + 0.1 + 0.35 + 0.17
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.65 + 0.17 = 0.82 ≠ 1
Therefore this is NOT a probability density function
c. x P(X=x)
0---- 9/10
1 ---- −3/10
2 ---- 3/10
3 ---- 1/10
Since P(X=1) is not between 0 and 1
Therefore this is NOT a probability density function
d. x P(X=x)
0 ----0.06
1 ----0.01
2 ----0.07
3 ----0.86
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.06 + 0.01 + 0.07 + 0.86
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.14 + 0.86 = 1
Therefore this is a probability density function
e. x P(X=x)
0 ----1/2
1 ----1/8
2 ----1/4
3 ----1/8
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/2 + 1/8 + 1/4 + 1/8
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/2 + 1/2 = 1
Therefore this is a probability density function
f. x P(X=x)
0 ----1/10
1 ----1/10
2 ----3/10
3 ----1/5
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/10 + 1/10 + 3/10 + 1/5
P(X=0)+P(X=1)+P(X=2)+P(X=3) = 2/10 + 5/10 = 7/10 ≠ 1
<h3>Therefore this is NOT a probability density function</h3>
