Statistics and Probability Answers

An airline knows that 5% of the people making reservations on a certain flight will
not turn up. Consequently their policy is to sell 52 tickets for a flight that can
accommodate only 50 passengers. What is the probability that there will be a seat
for every passenger who turns up?

The joint probability function of two discrete random variables X and Y is given by f(x ,y) = c(2x+y), where x and y can assume all integral values such that 0 ≤ x ≤ 2, 0 ≤ y ≤ 3, and f(x, y) = 0 otherwise. Find the value of the constant c, (ii) P(x=2, y=1), (iii) P(x≥1, y≤2), (iv) Marginal probability functions of X and Y. Check whether X and Y are independent.

An oil-drilling company knows that it costs $25,000 to sink a test well. If oil is hit, the income for the drilling company will be $335,000. If only natural gas is hit, the income will be $130,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and if the probability of hitting gas is 1/20, what is the expectation for the drilling company?

A communication channel transmit the digit 0 and 1 however due to static noise the digit transmit is incorrectly received with the probability 0.2 suppose we want to transmit the important message of one binary digit . to reduce the chance of error we transmit 00000 instead of 0 and 11111 instead of 1.If the receiver of message uses majority decoding what is the probability that the message will be incorrectly decoded

the public health official claim that home water use is 350 gallons a day to verify this claim 20 randomly selected homes was studied with the result that the mean is 53.8 with standard deviation 21.84

In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and standard deviation of the distribution

A company manufactures 4000 cars in a year with a probability that a part will be defective is
0.002. Find the probability that company produces
a) 4 cars with defective
b) atleast 4 cars
c) at most 4 cars with defective.

A Box contains 12 balls of which 3 are white and 9 are red. A sample of 3 balls is selected at
random from the box. Find the moment generating function of X and hence find mean and
standard deviation of the distribution.

10. A pair of dice is rolled 180 times. What is the probability that a total of six occurs
a) Atleast 30 times b)between 33 and 42 times inclusive. Use Normal approximation to Binomial distribution

The sales in a two wheeler showroom is exponentially distributed with mean equal to 4. If two days are selected at random, what is the probability that

a) on both days the sales is over 5 units
b) the sale is over 5 units on at least one of the
two days