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, $\frac{a}{b} = \frac{2}{1/30} = 60$.

Similar Questions

$A$ player tosses $2$ fair coins. He wins ₹ $5$ if $2$ heads appear,₹ $2$ if one head appears,and ₹ $1$ if no head appears. Then the variance of his winning amount in ₹ is

$A$ fair coin is tossed four times. $A$ person wins $Rs. 1$ for each head and loses $Rs. 1.50$ for each tail that turns up. From the sample space,calculate the different amounts of money one can have after four tosses and the probability of having each of these amounts.

If the probability that an individual will suffer a reaction from an injection of a drug is $0.001$, then the probability that out of $2000$ individuals having that injection, more than $2$ individuals will suffer a reaction, is

$A$ fair coin is tossed $4$ times. If $X$ is a random variable which indicates the number of heads,then $P[X < 3] = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module