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 values:${ }^4 C_4 p^4 q^0 = 6 \cdot { }^4 C_2 p^2 q^2$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$$p^4 = 36 p^2 q^2$Dividing both sides by $p^2$ (assuming $p 
eq 0$):$p^2 = 36 q^2$Taking the square root of both sides:$p = 6q$Substitute $q = 1-p$:$p = 6(1-p)$$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

The instantaneous values of alternating current and voltage in a circuit are given as $i = \frac{1}{\sqrt{2}} \sin(100\pi t) \text{ A}$ and $e = \frac{1}{\sqrt{2}} \sin(100\pi t + \frac{\pi}{3}) \text{ V}$. The average power in Watts consumed in the circuit is:

Aniline reacts with acetaldehyde to form

$A$ gas formed by the action of alcoholic $KOH$ on ethyl iodide,decolourises alkaline $KMnO_4$. The gas is

If $x$ is a solution of the equation $\sqrt{2x+1} - \sqrt{2x-1} = 1$ where $x \geq \frac{1}{2}$,then $\sqrt{4x^2-1}$ is equal to

The diameters of a circle are along $2x+y-7=0$ and $x+3y-11=0$. Then,the equation of this circle,which also passes through $(5,7)$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module