Chapter 5: Q.15 (page 347)

$f (x)$ a continuous probability function, is equal to $\frac{1}{3}$ and the function is restricted to $1 \leq x \leq 4$ . Describe $P (x > \frac{3}{2})$ .

Short Answer

Expert verified

The required probability is $P (x > \frac{3}{2})$ $= 0.83$

Step by step solution

Given Information

$f (x)$ a continuous probability function is equal to $\frac{1}{3}$ .

The function is restricted to $1 \leq x \leq 4$ .

We need to describe $P (x > \frac{3}{2})$

Calculation

Here $X$ follows a uniform distribution.

The area between $1 \leq x \leq 4$ forms a rectangle with $X$ axis

Here,

$Height = \frac{1}{3}$

$Base = 4 - \frac{3}{2}$

$= \frac{8 - 3}{2}$

$= 2.5$

Therefore, the required probability is,

$P (x > \frac{3}{2}) = Base \times Height$

$= (2.5) \times (\frac{1}{3})$

$= 0.83$

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$f (x)$ a continuous probability function, is equal to $\frac{1}{3}$ and the function is restricted to $1 \leq x \leq 4$ . Describe $P (x > \frac{3}{2})$ .

Short Answer

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$f (x)$ a continuous probability function, is equal to $\frac{1}{3}$ and the function is restricted to $1 \leq x \leq 4$ . Describe $P (x > \frac{3}{2})$ .