COMEDK 2024 Shift 1 Paper

To find the mean of the given probability distribution, we use the formula for the expected value of a discrete random variable. The expected value (mean) of X is given by:
E(X)=

∑

i

xi⋅P(X=xi)
Given the values:
X=xi:2,3,4,5

and corresponding probabilities:
P(X=xi):‌

5

k

,‌

7

k

,‌

9

k

,‌

11

k

First, we need to find the value of the constant k to ensure that the sum of the probabilities equals 1 :
‌

5

k

+‌

7

k

+‌

9

k

+‌

11

k

=1

Simplifying, we get:
‌

5+7+9+11

k

=1⟹‌

32

k

=1⟹k=32
With k=32, the probability values become:
Now we calculate the mean (expected value) E(X) :
‌E(X)=2⋅‌

5

32

+3⋅‌

7

32

+4⋅‌

9

32

+5⋅‌

11

32

‌E(X)=‌

10

32

+‌

21

32

+‌

36

32

+‌

55

32

‌E(X)=‌

10+21+36+55

32

‌E(X)=‌

122

32

‌E(X)=‌

61

16

So, the mean of this distribution is
Option A: ‌

61

16