$$\begin{aligned} &\text { The pdf of a random variable } X \text { is }\\ &\begin{aligned} f(x) & =3\left(1-2 x^2\right), & & 0< x<1 \\ & =0 & & \text { otherwise } \end{aligned} \end{aligned}$$

The $P\left(\frac{1}{4}< x<\frac{1}{3}\right)=\ldots$

A player tosses 2 fair coins. He wins Rs. 5 if 2 heads appear, Rs. 2 If 1 head appear and Rs. 1 if no head appears, then variance of his winning amount is

In a bionomial distribution, mean is 18 and variance is 12 then $p=$ ...........

The p.d.f of a random variable $x$ is given by

$$\begin{aligned} & f(x)=\frac{1}{4 a}, \quad 00) \\ & =0 \text {, otherwise } \end{aligned}$$

and $P\left(x<\frac{3 a}{2}\right)=k P\left(x>\frac{5 a}{2}\right)$ then $k=$ ..............