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:

If $X$ is a random variable which can assume values $0, 1, 2, 3$ or $4$ such that $P(X = 1) = P(X = 2)$ and $3P(X = 3) = 4P(X = 4) = P(X = 0) = \frac{1}{8}$, then $P(X > 0)$ is:

The normal distribution curve is symmetrical about

[$\mu$ = mean, $\sigma$= standard deviation]

When the doctor arrives late, what is the probability that he comes by metro?

A dice is thrown twice, the probability of occurence of 5 at least once is

Let A and B be two events. Then which of the following statements are TRUE?

(A) $P(B|A) = \frac{P(A \cap B)}{P(A)}$, provided $P(A) \neq 0$

(B) $P(B') = 1 + P(B)$

(C) $P(A \cup B) = P(A) + P(B) + P(A \cap B)$

(D) $P(A \cap B) = P(A).P(B)$ If A and B are independent events

Choose the correct answer from the options given below:

The probability distribution function of a normal variate with mean $\mu$ and variance $\sigma^2$ is given by:

$f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}$, $-\infty < x < \infty$, $-\infty < \mu < \infty$, $\sigma > 0$

If $y = f(x)$ be the normal probability curve, then which of the following is correct?

(A) The normal curve is symmetrical about the line $x = \mu$.

(B) Mean, median and mode of the distribution coincide.

(C) Y- axis is an asymptote to the normal curve.

(D) If x increases numerically, $f(x)$ decreases rapidly.

Choose the correct answer from the options given below: