Search & Filtering
if the moment generating function (m.g.f) of a random variable X is Mx (t) = exp(3t + 32t2) . find mean and standard deviation of X and also compute P(x<3)
We wish to estimate the mean serum indirect bilirubin level of 4-day-old infants. The mean for a sample of 16 infants was found to be 5.98 mg100 cc. Assume that bilirubin levels in 4-day-old infants are approximately normally distributed with a standard deviation of 3.5 mg100 cc.
Two dice are tossed. Let X = represent the sum of two dice Make a table of all possible values. Find the values of the random variable X.
A binary transmission system transmits a signal X ( to send a “000 bit; to send a “100 bit). The received signal is Y = X + N where noise N has a zero-mean Gaussian distribution with variance σ 2 . Assume that “000 bits are three times as likely as “100 bits. (i) Find the conditional pdf of Y given the input value: fY (y|X = +1) and fY (y|X = −1). (ii) The receiver decides a “000 was transmitted if the observed value of y satisfies fY (y|X = −1)P[X = −1] > fY (y|X = +1)P[X = +1] and it decides a “100 was transmitted otherwise. Use the results from part a to show that this decision rule is equivalent to: If y < T decide “000; if y <≥ T decide “100 . (iii) What is the probability that the receiver makes an error given that a +1 was transmitted? a −1 was transmitted? Assume σ 2 = 1/16. (iv) What is the overall probability of error?
Starting at 5:00 A.M., every half hour there is a train from city A to city B. Suppose that none of these trains is completely sold out and that they always have room for passengers. A person who wants to travel to city B arrives at the station at a random time between 8:45 A.M. and 9:45 A.M. Find the probability that he waits (a) at most 10 minutes; (b) at least 15 minutes.
Let Y = |Z|, where Z ∼ N (0, 1) be a discrete random variable with the following PMF: (i) Find E(Y ) and V ar(Y ). (ii) Find V ar(Y ). (iii) Find the CDF and PDF of Y .
Some amount of oil is spilled onto the surface of an ocean due to an oil-tanker accident. The oil spot then spreads away on the sea surface. The radius, R, of the oil spot in kilometers, 24 hours after the accident, has density function fR(r) = 3 4 {1 − (20 − r) 2 }, 19 ≤ r ≤ 20 Assuming that the area covered by the oil spot is circular, find the density function for the size of this area
Q(1) [10 Marks] [CLO2,C3] (a) The time required, in hours, to repair a car is a r.v. X with pdf fX(x) = c(4x − x 2 ), where 0 ≤ x ≤ 4. (i) Find the value of the constant c. (ii) Find the probability that for a car which arrives now at the garage, the amount of time needed to get repaired will be (a) at least one but less than three hours; (b) more than two hours.
(b) Let X be a r.v. whose pdf is: fX(x) = √ 1 2π exp ( − (x ^2) /2 ) , where −∞ < x < ∞. Determine the conditional pdf fX(x||x| ≤ 1).
The average daily sales of 700 branch office was rs 120 thousands and the standard deviation is rs 15,000 during the distribution to be normal how many branch have sale
Let D represet the defective cellphone and N the non-defective
