Determine the mean and variance of the random variable X having the following probability distribution.

X=x	1	2	3	4	5	6	7	8	9	10
P(x)	0.15	0.10	0.10	0.01	0.08	0.01	0.05	0.02	0.28	0.20

Suppose the life in hours of a radio tube has the probability density function
\(f(x)=\left\{\begin{array}{l} e^{-\frac{x}{100}}, \text { when } x \geq 100 \\ 0, \quad \text { when } x<100 \end{array}\right.\)
Find the mean of the life of a radio tube.

The probability function of a random variable X is given by
\(p(x)=\left\{\begin{array}{l} \frac{1}{4}, \text { for } x=-2 \\ \frac{1}{4}, \text { for } x=0 \\ \frac{1}{2}, \text { for } x=10 \\ 0, \text { elsewhere } \end{array}\right.\)
Evaluate the following probabilities.
P(\(\le\))0

The probability density function of a continuous random variable X is
\(f(x)=\left\{\begin{array}{l} a+b x^{2}, 0 \leq x \leq 1 \\ 0, \text { otherwise } \end{array}\right.\)
where a and b are some constants. Find
(i) a and b if E(X)\(\frac{3}{5}\)
(ii) Var(X).

The probability function of a random variable X is given by
\(p(x)=\left\{\begin{array}{l} \frac{1}{4}, \text { for } x=-2 \\ \frac{1}{4}, \text { for } x=0 \\ \frac{1}{2}, \text { for } x=10 \\ 0, \text { elsewhere } \end{array}\right.\)
Evaluate the following probabilities.
P(|X|\(\le\)2)