GATE (TF) Textile 2016 Question Paper Solution | GATE/2016/TF/28

Question 28 (Textile Engineering & Fibre Science)

Let ܺ $X$ be a continuous type random variable with probability density function $f(x)=\begin{cases} \frac{1}{4} & 1 \leq x\leq 3 \\ 0 & otherwise \end{cases}$ . When $P(X \leq x) = 0.75$ , the value of $x$ is equal to __1.99:2.01__.

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$f(x)=\begin{cases} \frac{1}{4} & 1 \leq x\leq 3 \\ 0 & otherwise \end{cases}$ . When $P(X \leq x) = 0.75$
X is a random variable
$\int_{-1}^{x} f(x) dx=0.75$
$\int_{-1}^{x} \frac{1}{4} dx=0.75$
$\frac{1}{4} \int_{-1}^{x} 1 dx=0.75$
$\frac{1}{4} [x]_{-1}^{x}=0.75$
[x+1]=0.75 x 4
x+1=3
x=2 (Ans)

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