A random variable X has the following probability distribution:
|
$X$ |
-2 |
-1 |
0 |
1 |
2 |
3 |
|
$P(X)$ |
0.1 |
0.2 |
$k$ |
0.3 |
$2k$ |
0.1 |
then which of the following are TRUE?
(A) $k=0.1$
(B) $P(X < 1) = 0.4$
(C) $P(X < 2) = 0.7$
(D) $P(0 < x < 3) = 0.5$
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B), (C) and (D) **
Given probabilities:
$0.1,\;0.2,\;k,\;0.3,\;2k,\;0.1$
Sum must be 1:
$0.1+0.2+k+0.3+2k+0.1 = 1$
$0.7 + 3k = 1$
$3k = 0.3$
$k = 0.1$ ✔
Now check statements:
(A) $k = 0.1$ ✔
(B) $P(X < 1) = P(-2)+P(-1)+P(0)$
$= 0.1 + 0.2 + 0.1 = 0.4$ ✔
(C) $P(X < 2) = P(-2) + P(-1) + P(0) + P(1)$
$= 0.1 + 0.2 + 0.1 + 0.3 = 0.7$ ✔
(D) $P(0 < X < 3) = P(1) + P(2)$
$= 0.3 + 0.2 = 0.5$ ✔
Correct statements: (A), (B), (C), (D)