88
MCQ (Single Correct Answer)
For the following probability distribution.
| $X$ | $-$4 | $-$3 | $-$2 | $-$1 | 0 |
|---|---|---|---|---|---|
| $P(X)$ | 0.1 | 0.2 | 0.3 | 0.2 | 0.2 |
E(X) is equal to
A
0
B
$-$1
C
$-$2
D
$-$1.8
89
MCQ (Single Correct Answer)
For the following probability distribution.
| $X$ | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| $P(X)$ | $\frac{1}{10}$ | $\frac{1}{5}$ | $\frac{3}{10}$ | $\frac{2}{5}$ |
$E\left(X^2\right)$ is equal to
A
3
B
5
C
7
D
10
90
MCQ (Single Correct Answer)
Suppose a random variable $X$ follows the Binomial distribution with parameters $n$ and $p$, where $0
A
$\frac{1}{2}$
B
$\frac{1}{3}$
C
$\frac{1}{5}$
D
$\frac{1}{7}$
91
MCQ (Single Correct Answer)
In a college, $30 \%$ students fail in Physics, $25 \%$ fail in Mathematics and $10 \%$ fail in both. One student is chosen at random. The probability that she fails in Physics, if she has failed in Mathematics is
A
$\frac{1}{10}$
B
$\frac{2}{5}$
C
$\frac{9}{20}$
D
$\frac{1}{3}$
92
MCQ (Single Correct Answer)
$A$ and $B$ are two students. Their chances of solving a problem correctly are $\frac{1}{3}$ and $\frac{1}{4}$, respectively. If the probability of their making a common error is, $\frac{1}{20}$ and they obtain the same answer, then the probability of their answer to be correct is
A
$\frac{1}{12}$
B
$\frac{1}{40}$
C
$\frac{13}{120}$
D
$\frac{10}{13}$