The graph of a function f(x) is shown in the figure.

For f(x) to be a valid probability density function, the value of h is

1/3

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2/3

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Solution

The correct option is A 1/3
If f(x) is valid density function then area under the curve should be 1

$\frac{1}{2} \times 1 \times h + \frac{1}{2} \times 1 \times 2 h + \frac{1}{2} \times 1 \times 3 h = 1$

$\frac{h}{2} + 2 h (\frac{1}{2}) + 3 h (\frac{1}{2}) = 1 \Rightarrow h = \frac{1}{3}$

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The graph of a function f(x) is shown in the figure. For f(x) to be a valid probability density function, the value of h is

The correct option is A 1/3If f(x) is valid density function then area under the curve should be 1 12×1×h+12×1×2h+12×1×3h=1 h2+2h(12)+3h(12)=1⇒h=13

The graph of a function f(x) is shown in the figure.

For f(x) to be a valid probability density function, the value of h is

The correct option is A 1/3
If f(x) is valid density function then area under the curve should be 1

$\frac{1}{2} \times 1 \times h + \frac{1}{2} \times 1 \times 2 h + \frac{1}{2} \times 1 \times 3 h = 1$

$\frac{h}{2} + 2 h (\frac{1}{2}) + 3 h (\frac{1}{2}) = 1 \Rightarrow h = \frac{1}{3}$