Statistics and Probability Answers

Verify that f(x,y)=xye^(-x)e^(-y),x>0,y>0 , satisfies the conditions necessary to be density for a continuous random variables x and Y. Are X and Y independent? Find the correlation coefficient.

The arrival of trucks on a receiving dock is a Poisson process with a mean arrival rate of two per hour. (a) Find the probability that exactly 5 trucks arrive in a three-hour period. (b) Find the probability that less than two will arrive in 4 hours.

The sales per day in a shop is exponentially distributed with average sale amounting to Rs.100 and net profit is 8%. Find the probability that the net profit exceeds Rs.30 on two consecutive days.

Please help me answer this question A box containing 8 light bulbs of which 3 are defective. A bulb is selected from the
box and tested. If it is defective, another bulb is selected and tested until a nondefective
bulb is chosen. Find the expected number and variance of bulbs chosen.

Steel rods are manufactured to be 3 inches in diameter but they are acceptable if they are inside the limit 2.99 inches and 3.01 inches. It is observed that 5% are rejected as oversized and 5% are rejected undersized. Assuming that the diameters are normally distributed, find the standard deviation of the distribution.

A survey was conducted in a slum locality of 2000 families by selecting a sample of size 800. It was revealed that 180 families were illiterates. Find the probable limits of the illiterate families in the population of 2000.

A survey was conducted in a slum locality of 2000 families by selecting a sample of size 800. It was revealed that 180 families were illiterates. Find the probable limits of the illiterate families in the population of 2000.

Steel rods are manufactured to be 3 inches in diameter but they are acceptable if they are inside the limit 2.99 inches and 3.01 inches. It is observed that 5% are rejected as oversized and 5% are rejected undersized. Assuming that the diameters are normally distributed, find the standard deviation of the distribution.

The sales per day in a shop is exponentially distributed with average sale amounting to Rs.100 and net profit is 8%. Find the probability that the net profit exceeds Rs.30 on two consecutive days.

In a test on 2500 electric bulbs, it was found that the life of a particular make was normally distributed with an average life of 2000 hours and S. D. of 60 hours. Estimate the number of bulbs likely to burn for (i) more than 2100 hours, (ii) less than 1950 hours and (iii) more than 1900 hours and but less than 2100 hours.