If the sum of the mean and the variance of a | vedclass

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

Question

(D) For a Binomial distribution with $n$ trials,the mean is $\mu = np$ and the variance is $\sigma^2 = npq$,where $q = 1 - p$.Given $n = 5$ and $\mu +

Vedclass · Accepted Answer

$0.2$

Vedclass · Answer

(D) For a Binomial distribution with $n$ trials,the mean is $\mu = np$ and the variance is $\sigma^2 = npq$,where $q = 1 - p$.Given $n = 5$ and $\mu + \sigma^2 = 1.8$.Substituting the values,we get:$np + npq = 1.8$$5p + 5p(1 - p) = 1.8$$5p + 5p - 5p^2 = 1.8$$10p - 5p^2 = 1.8$$5p^2 - 10p + 1.8 = 0$Multiplying by $10$ to clear the decimal:$50p^2 - 100p + 18 = 0$Dividing by $2$:$25p^2 - 50p + 9 = 0$Using the quadratic formula $p = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:$p = \frac{50 \pm \sqrt{2500 - 4(25)(9)}}{50} = \frac{50 \pm \sqrt{2500 - 900}}{50} = \frac{50 \pm \sqrt{1600}}{50} = \frac{50 \pm 40}{50}$$p_1 = \frac{90}{50} = 1.8$ (Not possible since $0 \le p \le 1$)$p_2 = \frac{10}{50} = 0.2$Thus,$p = 0.2$.

If the sum of the mean and the variance of a Binomial distribution for $5$ trials is $1.8$,then the value of $p$ is

Similar Questions

The mean and variance of a random variable $X$ having a binomial distribution are $6$ and $3$ respectively. The probability of variable $X$ less than $2$ is . . . . . . .

Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. Let $X$ denote the random variable of the number of jacks obtained in the two drawn cards. Then $P(X=1) + P(X=2)$ equals

$A$ die is thrown twice. If getting a number greater than $4$ on the die is considered a success,then the variance of the probability distribution of the number of successes is

$A$ lot of $100$ bulbs contains $10$ defective bulbs. Five bulbs are selected at random from the lot and are sent to a retail store. Then the probability that the store will receive at most one defective bulb is

If $X \sim B(4, p)$ and $2 P(X=3)=3 P(X=2)$,then the value of $p$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module