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  • Fill in the blanks in the following question: If X follows binomial distribution with parameters n = 5, p and P (X = 2) = 9.P (X = 3), then p = ___________

Fill in the blanks in the following question:
If X follows binomial distribution with parameters n = 5, p and P (X = 2) = 9.P (X = 3), then p = ___________

 

Answers (1)

p = 1/10

As n = 5 {representing no. of trials}

p = probability of success
As it is a binomial distribution.
∴ probability of failure = q = 1 – p
Given-
P(X = 2) = 9.P(X = 3)
The binomial distribution formula is:

\mathrm{P}(\mathrm{x})=^{n} \mathrm{C}_{x} \mathrm{P}^{\mathrm{x}}(1-\mathrm{P})^{\mathrm{n}-\mathrm{x}}$
 

Where:
x = total number of “successes.”
P = probability of success on an individual trial
n = number of trials
using binomial distribution,
\\\Rightarrow{ }^{5} \mathrm{C}_{2} \mathrm{p}^{2} \mathrm{q}^{5-2}=9^{5} \mathrm{C}_{3} \mathrm{p}^{3} \mathrm{q}^{5-3}$ \\$\Rightarrow 10 p^{2} q^{3}=9 \times 10 p^{3} q^{2}$ \\$\Rightarrow 10 q=90 p\{A s, p \neq 0$ and $q \neq 0\}$ \\$\Rightarrow q=9 p$ \\$\Rightarrow 1-p=9 p \Rightarrow 10 p=1$ \\$\therefore p=1 / 10$

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infoexpert22

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