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Question 4. [5 marksi Let Xbe a random variable with probability mass function (pmf) A-p for...
7. Let Xbe a discrete random variable with probability mass function: f(x) c , x 0,1,2,3,...
7. Let Xbe a discrete random variable with probability mass function: f(x) c , x 0,1,2,3, 4 (a) Find the constant c. (b) Find the moment generating function of X. (c) Find EX based on the result of part (b)
Consider a random variable X with RX = {−1, 0, 1} and PMF P(X = −1)...
Consider a random variable X with RX = {−1, 0, 1} and PMF P(X =
−1) = 1/4 , P(X = 0) = 1/2 , P(X = 1) = 1/4 .
a) Determine the moment-generating function (MGF) MX(t) of
X.
b) Obtain the first two derivatives of the MGF to compute E[X]
and Var(X).
Consider a random variable X with Rx = {-1,0,1} and PMF Determine the moment-generating function (MGF) Mx(t) of X b) Obtain the first two derivatives of...
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the...
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
5. Find the moment generating function of the continuous random variable X whose a. probability density...
5. Find the moment generating function of the continuous random variable X whose a. probability density is given by )-3 or 36 0 elsewhere find the values of μ and σ2. b, Let X have an exponential distribution with a mean of θ = 15 . Compute a. 6. P(10 < X <20); b. P(X>20), c. P(X>30X > 10), the variance and the moment generating function of x. d.
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27...
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27 0.2 0.1 0.03 0.15 0.1 a) Determine the b) Find P(X-Y>2). c) Find PX s3|Y20) d) Determine E(XY) e) Determine E(X) and E(Y). f) Are X and Y independent? marginal pmf for X and Y. Question 2 Let X and Y be independent random variables with pdf 2-y 0sxS 2 f(x)- f(p)- 0, otherwise 0, otherwise a) b) Find E(XY). Find Var (2X +...
6. The Poisson distribution is commonly used to model discrete data. The probability mass function of...
6. The Poisson distribution is commonly used to model discrete data. The probability mass function of a Poisson random variable is P(X = x/A) =ー厂 , x = 0, 1, 2, , λ > 0. a. Find the MGF of a Poisson random variable. b. Use the MGF to find the mean of a Poisson random variable c. Use the MGF to find the second raw moment of a Poisson random variable. d. Use results d. Let Xi and X2...
Suppose a random variable X has a pmf p(x) = [3^(x-1)] / [4^x] , x = 1,...
Suppose a random variable X has a pmf p(x) = [3^(x-1)] / [4^x] , x = 1, 2, ... (a) Find the moment generating function of X. (b) Give a realistic example of an experiment that this random variable can be defined from its sample space. (c) Find the mean and variance of X.
The moment generating function ф(t) of random variable X is defined for all values of t by et*p(x), if X is discrete e...
The moment generating function ф(t) of random variable X is defined for all values of t by et*p(x), if X is discrete e f (x)dx, if X is continus (a) Find the moment generating function of a Binomial random variable X with parameters n (the total number of trials) and p (the probability of success). (b) If X and Y are independent Binomial random variables with parameters (n1 p) and (n2, p), respectively, then what is the distribution of X...
(4 marks The moment generating function (mgf) of a random variable X is given by (a)...
(4 marks The moment generating function (mgf) of a random variable X is given by (a) Use the mgf to find the mean and variance of X (b) What is the probability that X = 2?
Let X, Y be independent random variables where X is binomial(n = 4, p = 1/3)...
Let X, Y be independent random variables where X is binomial(n = 4, p = 1/3) and Y is binomial(n = 3,p = 1/3). Find the moment-generating functions of the three random variables X, Y and X + Y . (You may look up the first two. The third follows from the first two and the behavior of moment-generating functions.) Now use the moment-generating function of X + Y to find the distribution of X + Y .
7. Let Xbe a discrete random variable with probability mass function: f(x) c , x 0,1,2,3, 4 (a) Find the constant c. (b) Find the moment generating function of X. (c) Find EX based on the result of part (b)
Consider a random variable X with RX = {−1, 0, 1} and PMF P(X =
−1) = 1/4 , P(X = 0) = 1/2 , P(X = 1) = 1/4 .
a) Determine the moment-generating function (MGF) MX(t) of
X.
b) Obtain the first two derivatives of the MGF to compute E[X]
and Var(X).
Consider a random variable X with Rx = {-1,0,1} and PMF Determine the moment-generating function (MGF) Mx(t) of X b) Obtain the first two derivatives of...
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
5. Find the moment generating function of the continuous random variable X whose a. probability density is given by )-3 or 36 0 elsewhere find the values of μ and σ2. b, Let X have an exponential distribution with a mean of θ = 15 . Compute a. 6. P(10 < X <20); b. P(X>20), c. P(X>30X > 10), the variance and the moment generating function of x. d.
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27 0.2 0.1 0.03 0.15 0.1 a) Determine the b) Find P(X-Y>2). c) Find PX s3|Y20) d) Determine E(XY) e) Determine E(X) and E(Y). f) Are X and Y independent? marginal pmf for X and Y. Question 2 Let X and Y be independent random variables with pdf 2-y 0sxS 2 f(x)- f(p)- 0, otherwise 0, otherwise a) b) Find E(XY). Find Var (2X +...
6. The Poisson distribution is commonly used to model discrete data. The probability mass function of a Poisson random variable is P(X = x/A) =ー厂 , x = 0, 1, 2, , λ > 0. a. Find the MGF of a Poisson random variable. b. Use the MGF to find the mean of a Poisson random variable c. Use the MGF to find the second raw moment of a Poisson random variable. d. Use results d. Let Xi and X2...
The moment generating function ф(t) of random variable X is defined for all values of t by et*p(x), if X is discrete e f (x)dx, if X is continus (a) Find the moment generating function of a Binomial random variable X with parameters n (the total number of trials) and p (the probability of success). (b) If X and Y are independent Binomial random variables with parameters (n1 p) and (n2, p), respectively, then what is the distribution of X...
(4 marks The moment generating function (mgf) of a random variable X is given by (a) Use the mgf to find the mean and variance of X (b) What is the probability that X = 2?
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