Question

For the probability distribution

x:	0	1	2	3	4	5
p(x) :	k	0.3	0.15	0.15	0.1	2 k

The expected value of X is

• A. 1.45
• B. 2.45
• C. 1.55
• D. 2.55

Answer 1

Answer: (B)

2.45

Answer 2

To find the expected value, first determine the value of k using the fact that the sum of all probabilities must equal 1.

So, we have:

$k + 0.3 + 0.15 + 0.15 + 0.1 + 2k = 1$

Combining terms:

$3k + 0.7 = 1$

Solving for k:

$3k = 0.3$

$k = 0.1$

Now that we have the value of k, we can calculate the expected value $E(X)$ using the formula:

$E(X) = \sum x \cdot p(x)$

$E(X) = (0 \cdot k) + (1 \cdot 0.3) + (2 \cdot 0.15) + (3 \cdot 0.15) + (4 \cdot 0.1) + (5 \cdot 2k)$

Substitute $k = 0.1$:

$E(X) = (0 \cdot 0.1) + (1 \cdot 0.3) + (2 \cdot 0.15) + (3 \cdot 0.15) + (4 \cdot 0.1) + (5 \cdot 2 \cdot 0.1)$

$E(X) = 0 + 0.3 + 0.3 + 0.45 + 0.4 + 1.0$

$E(X) = 2.45$

Thus, the expected value of X is 2.45.