# For the following probability distribution: X 1 2 3 4 P(X) 110 310 310 25 E(X2) is equal to ______.

+1 vote
in General

For the following probability distribution:

| X | 1 | 2 | 3 | 4 |
| P(X) | $1/10$ | $3/10$ | $3/10$ | $2/5$ |

E(X2) is equal to ______.

• 3
• 5
• 7
• 10

by kratos

For the following probability distribution:

| X | 1 | 2 | 3 | 4 |
| P(X) | $1/10$ | $3/10$ | $3/10$ | $2/5$ |

E(X2) is equal to 10.

Explanation:

We know that

E(X2) = $sum_("i" = 1)^"n" "P"_"i""X"_"i"^2$

= $1 xx 1/10 + 4 xx 1/5 + 9 xx 3/10 + 16 xx 2/5$

= $1/10 + 4/5 + 27/10 + 32/5$

= $28/10 + 36/5$

= $100/10$

= 10