Probability that the duration is between 5 and seven minutes

Assignment Help Basic Statistics

Reference no: EM132170241

Question 1

a) A cell-phone tower has a circular coverage area of radius 10 Km. If a call is initiated from a random point in the coverage area, find the probability that the call comes from within 2 Km of the tower.

b) Consider the duration of a cell-phone call. For the sample space Ω = [0, ∞), find the probability that the duration is between 5 and seven minutes.

c) Three bits are transmited across a noisy channel and the number of correct receptions is noted. Find the probability that the number of correctly received bits is two, assuming bit errors are mutually independent and that on each transmission the probability of correct reception is λ for some fixed 0 ≤ λ ≤ 1.

d) The number of hits to a popular website during a 1-minute interval is given by Xi random variable. Find the probability that there is at least one hit between 3:00 a.m and 3:01 a.m if rate prameter is 2 hits per minute. Then find the probability that there are at least 2
hits during this time interval.

Question 2

a) The probability function for random variable X is

f(x) = {2^-x, x = 1,2, . .
{ 0, otherwise
Find the probability function of a random variable U = X⁴ + 1.

b) The probability function of a random variable X is given by

{ x²/18, -3 < x < 6

f(x) = { 0, otherwise

Find the probability function for the random variable U = 1/3 (12 - X).

Reference no: EM132170241

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