Three Machines A, B, C Produce kind of Electronic Toy

Assignment Task

1. Three machine men A,B,C produces a special kind of electronic – toy, with respective probabilities 0.02,0.03 and 0.05 it fails to be established in market. In the factory where they work, A produces 50% of all toys, B 30% and C 20%. What proportion of “non-establishment is caused by A?

2. The spectrum of the random variable X consists of the points 1,2,...,n and P(X=i) is proportional to .Determine the distribution function of X.

3. A discrete random variable X has the following probability distribution

(i) find K

(ii) Find the minimum value of k such that P(X>=2)>=0.8

(iii) Determine the distribution function F(x)of X.                                          

4. A bank receives on an average 2.5 customers per hour. Find the probability that in a certain hour the bank receives (i) no customer (ii) exactly 4 customers. Assume that the number of customers received in an hour is poisson distributed.[ e^-2.5 = 0.0821]?

5. A and B toss a coin alternately and the first to obtain a head wins the toss.If A stars the game ,find the probability of his winning?

6. A  discrete random variable X has the mean 6 and variance 2.Assuming the distribution is binomial ,find the probability that 5 < X>

7. Afamily has 6 children. Find the probability that (i) 3 boys and 3 girls (ii) fewer boys than girls.

8. The bivariate (X,Y) is such that it take the values(i,j) where i=0,1,2,3; j=1,2,3,4. The joint probabilities P = (x = i, Y= j) = K (3i + 4j) (i) Find the value of k  (ii) P(x >2 y <3>

9. Show by Chebycheff’s inequality that in 2000 throwswith a coin the probability that the number of heads lies between 900 and 1100 is at least 19/20 .

10. If 10 unbiased dice are tossed. Find the approximate probability that the sum obtained is between 30 and 40, inclusive.

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