Lifetime of an electric bulb is a random variable with density $f (x) = k x^{2},$ where x is measured in years. If the minimum and maximum lifetimes of bulb are 1 and 2 years respectively, then the value of k is _____.

0.428

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Solution

The correct option is A 0.428
Given function is
$f (x) = k x^{2}, 1 < x < 2$

Since f(x) is a p.d.f, we have

$\int_{- \infty}^{\infty} f (x) d x = 1$

$\Rightarrow \int_{1}^{2} k x^{2} d x = 1$

$k {[\frac{x^{3}}{3}]}_{1}^{2} = 1$

k = 3/7

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Lifetime of an electric bulb is a random variable with density f(x)=kx2, where x is measured in years. If the minimum and maximum lifetimes of bulb are 1 and 2 years respectively, then the value of k is _____. 0.428

The correct option is A 0.428Given function is f(x)=kx2, 1<x<2 Since f(x) is a p.d.f, we have ∫∞−∞f(x)dx=1 ⇒ ∫21kx2dx=1 k[x33]21=1 k = 3/7

Lifetime of an electric bulb is a random variable with density $f (x) = k x^{2},$ where x is measured in years. If the minimum and maximum lifetimes of bulb are 1 and 2 years respectively, then the value of k is _____.

0.428

The correct option is A 0.428
Given function is
$f (x) = k x^{2}, 1 < x < 2$

Since f(x) is a p.d.f, we have

$\int_{- \infty}^{\infty} f (x) d x = 1$

$\Rightarrow \int_{1}^{2} k x^{2} d x = 1$

$k {[\frac{x^{3}}{3}]}_{1}^{2} = 1$

k = 3/7