Question

The probability of a component's failure is 0.05. Out of 14 components what is the probability distribution of X.
hint:binomial distribution​

Answer 1

Given :  The probability of a component's failure is 0.05

To find : Out of 14 components what is the probability distribution of X.

Solution

P(x) = ⁿCₓpˣqⁿ⁻ˣ

n = 14

p = 0.05

q = 1 - p = 1 -0.05 = 0.95

X                      P(x)

0                     ¹⁴C₀(0.05)⁰(0.95)¹⁴

1                     ¹⁴C₁(0.05)¹(0.95)¹³

2                     ¹⁴C₂(0.05)²(0.95)¹²

3                     ¹⁴C₃(0.05)³(0.95)¹¹

4                     ¹⁴C₄(0.05)⁴(0.95)¹⁰

5                     ¹⁴C₅(0.05)⁵(0.95)⁹

6                     ¹⁴C₆(0.05)⁶(0.95)⁸

7                     ¹⁴C₇(0.05)⁷(0.95)⁷

8                     ¹⁴C₈(0.05)⁸(0.95)⁶

9                     ¹⁴C₉(0.05)⁹(0.95)⁵

10                     ¹⁴C₁₀(0.05)¹⁰(0.95)⁴

11                     ¹⁴C₁₁(0.05)¹¹(0.95)³

12                     ¹⁴C₁₂(0.05)¹²(0.95)²

13                     ¹⁴C₁₃(0.05)¹³(0.95)¹

14                     ¹⁴C₁₄(0.05)¹⁴(0.95)⁰

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