A pair of dice is thrown l0 times. If getting a sum 10 is success, find the probability of
(i) 10 success
(ii) No success
(iii) More than 8 success

The probability function of a random variable X is f(x) \(=\mathrm{Ce}^{-|x|},-\infty<\mathrm{x}<\infty\) . Find the value of C and also find the mean and variance for the random variable.

An urn contains 4 Green and 3 Red balls. Find the probability distribution of the number of red balls in 3 draws when a baII is drawn at random with replacement. Also find its mean and variance.

For the distribution function given by \(\mathrm{F}(\mathrm{X})=\left\{\begin{array}{l} 0, x<0 \\ x^{2}, 0 \leq x \leq 1 \\ 1, x>1 \end{array}\right.\)find the density function, also evaluate
(i) P(X < 0.3)
(ii) P(X > 0.9)
(iii) P(0.1 < X < 0.5)

For the probability density function \(f(x)=\left\{\begin{array}{c} k(1-x)^{3}, 0<x<1 \\ 0, \text { elsewhere } \end{array}\right.\). Find 
(i) The constant k
(ii) \(P\left(X<\frac{2}{3}\right)\)

Raja wants to celebrate his birthday with his friends. He brought a cake box, holding 2 Butter Cake along with 8 Apple Cake. He took 2 cakes and gave it to his 2 friends. Obtain the probability mass function for number of butter cakes

A urn contains 5 white and 3 black chips. Find the probability distribution of number of black chips in three draws one by one from the urn without replacement.

A discrete random variable X has the following probability distributions

X	0	1	2	3
f(x)	a	3a	5a	7a

(i) Find the value of a
(ii) \(\mathbf{P}(\mathbf{X} \leq 1)\)

If \(f(x)= \begin{cases}\mathrm{Ax}, & 0<x<5 \\ \mathrm{~A}(10-x), & 5 \leq x<10\end{cases}\) is a p.d.f. of a continuous random variable X, then find its mean.

Two cards are drawn successively with replacement for a well shuffled pack of 52 cards. Find the probability distribution of the number of kings.

A random variable X has the following probability distribution values of X.

x	0	1	2	3	4	5	6	7
f(x)	0	k	2k	2k	3k	k2	2k2	\(7 k^{2}+k\)

Find 
(i) k
(ii) P(X<6)
(iii) \(P(X \geq 6)\)
(iv) P(0 < X<5)

A fair coin is tossed until a head or 5 tails occur. If X denote the number of tosses of the coin, find the mean of X.

For the distribution function given by \(\mathrm{F}(x)= \begin{cases}0, & x<0 \\ x^{2}, & 0 \leq x \leq 1 \\ 1, & x>1\end{cases}\). Find the density function. Also evaluate
\( (i) \ \mathrm{P}(0.5<x<0.75) \)
\( (ii) \ \mathrm{P}(x \leq 0.5) \)
\( (iii)\ \mathrm{P}(\mathrm{X}>0.75) \)