For a binomial variate X,if n=4 and P(X=4)=6 | vedclass

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

Question

(C) The probability mass function for a binomial distribution is given by $P(X=k) = { }^n C_k p^k q^{n-k}$,where $q = 1-p$.Given $n=4$,the equation is

Vedclass · Accepted Answer

$\frac{6}{7}$

Vedclass · Answer

(C) The probability mass function for a binomial distribution is given by $P(X=k) = { }^n C_k p^k q^{n-k}$,where $q = 1-p$.Given $n=4$,the equation is $P(X=4) = 6 P(X=2)$.Substituting the formula: ${ }^4 C_4 p^4 q^0 = 6 \cdot { }^4 C_2 p^2 q^2$.Since ${ }^4 C_4 = 1$ and ${ }^4 C_2 = \frac{4 	imes 3}{2 	imes 1} = 6$,we have:$1 \cdot p^4 = 6 \cdot 6 \cdot p^2 q^2$.$p^4 = 36 p^2 q^2$.Dividing both sides by $p^2$ (assuming $p 
eq 0$):$p^2 = 36 q^2$.Taking the square root of both sides:$p = 6q$ (since $p$ and $q$ are probabilities,they must be positive).Substitute $q = 1-p$:$p = 6(1-p)$.$p = 6 - 6p$.$7p = 6$.$p = \frac{6}{7}$.

For a binomial variate $X$,if $n=4$ and $P(X=4)=6 P(X=2)$,then the value of $p$ is

Similar Questions

When employees with smart phones are randomly selected,$50 \%$ use them for office purpose. The probability that out of $10$ users exactly $2$ of them use for office purpose is

In a binomial distribution,the probability of success is $\frac{1}{4}$ and the standard deviation is $3$. Find its mean.

$A$ medicine for fever can cure $75\%$ of the people. Three people suffering from fever use this medicine. What is the probability that all three people are cured?

When success is not an impossible event,then the mean of Binomial distribution is

In a binomial distribution,if $n=4$ and $P(X=0)=\frac{16}{81}$,then $P(X=4)=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module