A random variable X takes values 0, 1, 2, 3 w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The sum of probabilities must be $1$: $\frac{2a + 1}{30} + \frac{8a - 1}{30} + \frac{4a + 1}{30} + b = 1$ $\frac{14a + 1}{30} + b = 1 \Rightarrow

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(C) The sum of probabilities must be $1$: $\frac{2a + 1}{30} + \frac{8a - 1}{30} + \frac{4a + 1}{30} + b = 1$ $\frac{14a + 1}{30} + b = 1 \Rightarrow 14a + 30b = 29 \dots (1)$ We are given $\sigma^{2} + \mu^{2} = 2$. Since $\sigma^{2} = E[X^{2}] - \mu^{2}$,we have $E[X^{2}] = 2$. $E[X^{2}] = \sum x_{i}^{2} p(x_{i}) = 0^{2} \cdot \frac{2a+1}{30} + 1^{2} \cdot \frac{8a-1}{30} + 2^{2} \cdot \frac{4a+1}{30} + 3^{2} \cdot b = 2$ $\frac{8a - 1 + 16a + 4}{30} + 9b = 2$ $\frac{24a + 3}{30} + 9b = 2$ $\Rightarrow 24a + 3 + 270b = 60$ $\Rightarrow 24a + 270b = 57$ Dividing by $3$: $8a + 90b = 19 \dots (2)$ From $(1)$,$30b = 29 - 14a$. Substitute into $(2)$: $8a + 3(29 - 14a) = 19$ $8a + 87 - 42a = 19$ $-34a = -68 \Rightarrow a = 2$ Substituting $a = 2$ into $(1)$: $14(2) + 30b = 29$ $\Rightarrow 28 + 30b = 29$ $\Rightarrow 30b = 1$ $\Rightarrow b = \frac{1}{30}$ Therefore,$\frac{a}{b} = \frac{2}{1/30} = 60$.

$X$	$1, 2, 3, 4, 5$
$P(X)$	$K^2, 2K, K, 2K, 5K^2$

$X$	$30$	$10$	$-10$
$P(X)$	$\frac{1}{5}$	$A$	$B$

$X=x_i$	$-2$	$-1$	$0$	$1$	$2$
$P(X=x_i)$	$1/6$	$k$	$1/4$	$k$	$1/6$

Similar Questions

From a bag containing $4$ white and $5$ red balls,if $3$ balls are drawn at random,then the mean of the number of red balls among the balls drawn is:

$A$ random variable $X$ has the following probability distribution:
$X$ $1, 2, 3, 4, 5$
$P(X)$ $K^2, 2K, K, 2K, 5K^2$

Then $P(X > 2)$ is equal to:

Let $X$ be a discrete random variable. The probability distribution of $X$ is given below:
$X$ $30$ $10$ $-10$
$P(X)$ $\frac{1}{5}$ $A$ $B$

If $E(X) = 4$,then the value of $AB$ is equal to:

$A$ random variable $X$ has the following probability distribution:

$X=x_i$ $-2$ $-1$ $0$ $1$ $2$

$P(X=x_i)$ $1/6$ $k$ $1/4$ $k$ $1/6$

The variance of this random variable is

Vedclass Test Series

Exam Paper Generator

Online Exam Module