Question

In: Statistics and Probability

Let ? be the number of participants in a random meeting. The probability mass function of...

Let ? be the number of participants in a random meeting. The probability mass function of ? is given below. Assume that the meetings are independent.

0.5 for ? = 2

?(?) = 0.2 for ? = 4

0.3 for ? = 8

a) Find the mean and variance of ?.

b) What is the probability that the total number of participants in two meetings is exactly 10?

c) What is the probability that the number of participants in one meeting is fewer than 5?

d) What is the probability that the average number of participants in ten meetings is fewer than 5?

e) What is the probability that at least two out of ten meetings have less than 5 participants?

Solutions

Expert Solution

a)

Mean =

Also,

So,

b)

Let X1 and X2 denote the number of participants in 1st and 2nd meeting respectively.

Required probability =

c)

Required probability =

d)

Using Normal approximation,

Using Central Limit theorem, we know,

Required probability =

e)

Let Y denote the number of meeting that have fewer than 5 participants.

Then

Required probability =


orchestra answered 1 year ago
Next > < Previous

Related Solutions

Let X1 and X2 be a random sample from a population having probability mass function f(x=0)...
Let X1 and X2 be a random sample from a population having probability mass function f(x=0) = 1/3 and f(x=1) = 2/3; the support is x=0,1. a) Find the probability mass function of the sample mean. Note that this is also called the sampling distribution of the mean. b) Find the probability mass function of the sample median. Note that this is also called the sampling distribution of the median. c) Find the probability mass function of the sample geometric...
Plot the probability mass function (PMF) and the cumulative distribution function (CDF) of 3 random variables...
Plot the probability mass function (PMF) and the cumulative distribution function (CDF) of 3 random variables following (1) binomial distribution [p,n], (2) a geometric distribution [p], and (3) Poisson distribution [?]. You have to consider two sets of parameters per distribution which can be chosen arbitrarily. The following steps can be followed: Setp1: Establish two sets of parameters of the distribution: For Geometric and Poisson distributions take two values of p (p1 and p2) and take two values of [?],...
Plot the probability mass function (PMF) and the cumulative distribution function (CDF) of 3 random variables...
Plot the probability mass function (PMF) and the cumulative distribution function (CDF) of 3 random variables following (1) binomial distribution [p,n], (2) a geometric distribution [p], and (3) Poisson distribution [?]. You have to consider two sets of parameters per distribution which can be chosen arbitrarily. The following steps can be followed
Plot the probability mass function (PMF) and the cumulative distribution function (CDF) of 3 random variables...
Plot the probability mass function (PMF) and the cumulative distribution function (CDF) of 3 random variables following (1) binomial distribution [p,n], (2) a geometric distribution [p], and (3) Poisson distribution [?]. You have to consider two sets of parameters per distribution which can be chosen arbitrarily. The following steps can be followed: Setp1: Establish two sets of parameters of the distribution: For Geometric and Poisson distributions take two values of p (p1 and p2) and take two values of [?],...
Let Y be a discrete random variable with probability mass function given by P(Y =i)=c·(i−2) fori=3,4,6...
Let Y be a discrete random variable with probability mass function given by P(Y =i)=c·(i−2) fori=3,4,6 1. Pay attention to the possible values for Y , and find the numerical value of c. Make sure to show work / justify your answer. 2. Draw the graph of the cumulative distribution function of Y.
Let X and Y be two continuous random variables with the joint probability density function of...
Let X and Y be two continuous random variables with the joint probability density function of for 0 < x < 2, 0 < y < 2, x + y < 1,where c is a constant. (In all the following answers, you do NOT need to find what the value of c is; just treat it as a number.) (a) Write out the marginal distribution of Y. (b) P(Y < 1/3) = ? (c) P(X < 1.5, Y < 0.5)=...
Let X be a continuous random variable with a probability density function fX (x) = 2xI...
Let X be a continuous random variable with a probability density function fX (x) = 2xI (0,1) (x) and let it be the function´ Y (x) = e −x a. Find the expression for the probability density function fY (y). b. Find the domain of the probability density function fY (y).
. Let X and Y be a random variables with the joint probability density function fX,Y...
. Let X and Y be a random variables with the joint probability density function fX,Y (x, y) = { 1, 0 < x, y < 1 0, otherwise } . a. Let W = max(X, Y ) Compute the probability density function of W. b. Let U = min(X, Y ) Compute the probability density function of U. c. Compute the probability density function of X + Y ..
Let n be a random number between 1 and 100000 chosen with uniform probability. Compute a)...
Let n be a random number between 1 and 100000 chosen with uniform probability. Compute a) The probability that n can be divided by 3 b) The probability that n can be divided by 6 c) The probability that n can be divided by 9 d) The probability that n can be divided by 9 given that in can be divided by 6 e) The probability that n can be divided by 6 given that in can be divided by...
X1 and X2 are two discrete random variables. The joint probability mass function of X1 and...
X1 and X2 are two discrete random variables. The joint probability mass function of X1 and X2, p(x1,x2) = P(X1 = 1,X2 = x2), is given by p(1, 1) = 0.025, p(1, 2) = 0.12, p(1, 3) = 0.21 p(2, 1) = 0.18, p(2, 2) = 0.16, p(2, 3) = c. and p(x1, x2) = 0 otherwise. (a) Find the value of c. (b) Find the marginal probability mass functions of X1 and X2. (c) Are X1 and X2 independent?...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT