Two unbiased dice are thrown simultaneously and sum of the upturned faces considered as random variable. Construct a probability mass function.

The following table is describing about the probability mass function of the random variable X

x	3	4	5
P(x)	0.1	0.1	0.2

Find the standard deviation of x.

The number of miles an automobile tire lasts before it reaches a critical point in tread wear can be represented by a p.d.f.
\(f(x)= \begin{cases}\frac{1}{30} e^{-\frac{x}{30}}, & \text { for } x>0 \\ 0, & \text { for } x \leq 0\end{cases}\)
Find the expected number of miles (in thousands) a tire would last until it reaches the critical tread wear point.

The probability distribution function of a discrete random variable X is
\(F(x)=\left\{\begin{array}{l} 2k, x = 1 \\ 3k, x = 3 \\ 4k, x = 5 \\ 0, \text{otherwise} \end{array}\right.\)
where k is some constant. Find (a) k and (b) P(X>2).

Consider a random variable X with p.d.f
\(f(x)=\left\{\begin{array}{l} 3 x^{2}, \text { if } 0< x< 1 \\ 0, \text { otherwise } \end{array}\right.\)
Find E(X) and V(3X-2).