If X is a Poisson variate such that P(X=1)=2 | vedclass

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

Question

(A) For a Poisson distribution, the probability mass function is given by $P(X=x) = \frac{\lambda^x e^{-\lambda}}{x!}$.Given $P(X=1) = 2 P(X=2)$.Subst

Vedclass · Accepted Answer

$\frac{e^{-1}}{6}$

Vedclass · Answer

(A) For a Poisson distribution, the probability mass function is given by $P(X=x) = \frac{\lambda^x e^{-\lambda}}{x!}$.Given $P(X=1) = 2 P(X=2)$.Substituting the formula:$\frac{\lambda^1 e^{-\lambda}}{1!} = 2 	imes \frac{\lambda^2 e^{-\lambda}}{2!}$$\lambda e^{-\lambda} = 2 	imes \frac{\lambda^2 e^{-\lambda}}{2}$$\lambda e^{-\lambda} = \lambda^2 e^{-\lambda}$Since $\lambda > 0$ and $e^{-\lambda} 
eq 0$, we divide both sides by $\lambda e^{-\lambda}$:$1 = \lambda$Thus, the parameter $\lambda = 1$.Now, we calculate $P(X=3)$:$P(X=3) = \frac{\lambda^3 e^{-\lambda}}{3!} = \frac{1^3 e^{-1}}{6} = \frac{e^{-1}}{6}$.

If $X$ is a Poisson variate such that $P(X=1)=2 P(X=2)$, then $P(X=3)$ is equal to

Similar Questions

When the angle of incidence is $60^{\circ}$ on the surface of a glass slab,it is found that the reflected ray is completely polarized. The velocity of light in glass is

The sum of the fourth powers of the roots of the equation $x^3+x+1=0$ is

What is the volume (in litres) of oxygen at $STP$ required for complete combustion of $32 \ g$ of $CH_4$ ? (Molecular weight of $CH_4$ is $16$ )

The major product of the following reaction is:

What does an $ECG$ measure?

Vedclass Test Series

Exam Paper Generator

Online Exam Module