Please explain where does the
"e^-2" come from
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Please explain where does the
"e^-2" come from
Consider a discrete random variable whose PMF is...
Let X denote a discrete random variable with pmf of px (1) 75 and pr (2)...
Let X denote a discrete random variable with pmf of px (1) 75 and pr (2) = .25. When the random variable X is transmitted, the
Ciule jolh! PMF and the marginal PMFs? 6.14 Let X and Y be discrete random variables. Show that t...
ciule jolh! PMF and the marginal PMFs? 6.14 Let X and Y be discrete random variables. Show that the function p: R2 R defined by p(r, y) px(x)pr(y) is a joint PMF by verifying that it satisfies properties (a)-(c) of Proposition 6.1 on page 262. Hint: A subset of a countable set is countable CHAPTER SIX Joindy Discrete Random Variables 6.2 Joint and marginal PMFs of the discrete random variables x numher of bedrooms and momber of bwthrooms of a...
Let X be a discrete random variable whose distribution is given by the table below. W,...
Let X be a discrete random variable whose distribution is given by the table below. W, P(X=w 2 0.01 4 0.40 9 0.32 11 0.27 (the probability that X equals a number outside of the left column is zero) Calculate: 1. E(X) 2 Var(x) 3. PX <4)
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random...
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from this distribution: {2,3,10}. a. Find the method of moments estimate for 0 HINT: a very useful fact is that k1 n(n+1) 2 b. Find the MLE for 0 c. Which estimator is unbiased? d. Which estimator is preferred?
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from...
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0...
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2,...
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2, 3,..The moment generating function for this kind of random variable is M(t)Pe 1-(1-P)et. (a) What is E(X)? O p(1-P) 1-P (a) What is Var(x)? 1-p p2 p(1-P) O p(1-P) o -p
Where does epsilon come from in the lim e^n part? is it acting as for the...
Where does epsilon come from in the lim e^n
part? is it acting as
for the exponential distribution?
Example 7.8 Let XnExponential(n), show that Xn + 0. That is, the sequence X1, X2, X3, ... converges in probability to the zero random variable X. Solution We have lim P(|Xn -01 > €) = lim P(Xn > €) n-00 100 lim e-ne n->00 = 0, for all e > 0. (since Xn > 0) (since XnExponential(n)) We were unable to transcribe...
NOTE: DO PART b) ONLY 2. A discrete random variable X has the following pmf: A...
NOTE: DO PART b) ONLY
2. A discrete random variable X has the following pmf: A random sample of size n = 30 produced the following observations 1,3,0,00, 2, 22,0,1,2,0 1,1,0,1,1, 3, î021, 3. i 20.3.0, 2, i, (a) (i) Find and s for this sample. (ii) Find E(X) and var(X) (iii) Find the method of moments estimate of θ iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the inaximum likelihood...
NOTE: DO Part b) ONLY 2. A discrete random variable X has the following pmf: A...
NOTE: DO Part b) ONLY
2. A discrete random variable X has the following pmf: A random sample of size n = 30 produced the following observations 1,3,0,00, 2, 22,0,1,2,0 1,1,0,1,1, 3, î021, 3. i 20.3.0, 2, i, (a) (i) Find and s for this sample. (ii) Find E(X) and var(X) (iii) Find the method of moments estimate of θ iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the inaximum likelihood...
(a) Below is the CDF for a discrete random variable, X if x 1 1/2 if...
(a) Below is the CDF for a discrete random variable, X if x 1 1/2 if 1 x< 2 if 2 x 3 7/8 if 3 x 4 F(x) = 3/4 2 1 if nx <n+1. Describe the probability 2n In general, note that for any positive integer n, F(x) distribution of X by finding P(X 1), P(X = 2), P(X positive integer n, and describe an experiment that would result in this random variable X. 3), and the general...
Let X denote a discrete random variable with pmf of px (1) 75 and pr (2) = .25. When the random variable X is transmitted, the
ciule jolh! PMF and the marginal PMFs? 6.14 Let X and Y be discrete random variables. Show that the function p: R2 R defined by p(r, y) px(x)pr(y) is a joint PMF by verifying that it satisfies properties (a)-(c) of Proposition 6.1 on page 262. Hint: A subset of a countable set is countable CHAPTER SIX Joindy Discrete Random Variables 6.2 Joint and marginal PMFs of the discrete random variables x numher of bedrooms and momber of bwthrooms of a...
Let X be a discrete random variable whose distribution is given by the table below. W, P(X=w 2 0.01 4 0.40 9 0.32 11 0.27 (the probability that X equals a number outside of the left column is zero) Calculate: 1. E(X) 2 Var(x) 3. PX <4)
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from this distribution: {2,3,10}. a. Find the method of moments estimate for 0 HINT: a very useful fact is that k1 n(n+1) 2 b. Find the MLE for 0 c. Which estimator is unbiased? d. Which estimator is preferred?
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from...
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2, 3,..The moment generating function for this kind of random variable is M(t)Pe 1-(1-P)et. (a) What is E(X)? O p(1-P) 1-P (a) What is Var(x)? 1-p p2 p(1-P) O p(1-P) o -p
Where does epsilon come from in the lim e^n
part? is it acting as
for the exponential distribution?
Example 7.8 Let XnExponential(n), show that Xn + 0. That is, the sequence X1, X2, X3, ... converges in probability to the zero random variable X. Solution We have lim P(|Xn -01 > €) = lim P(Xn > €) n-00 100 lim e-ne n->00 = 0, for all e > 0. (since Xn > 0) (since XnExponential(n)) We were unable to transcribe...
NOTE: DO PART b) ONLY
2. A discrete random variable X has the following pmf: A random sample of size n = 30 produced the following observations 1,3,0,00, 2, 22,0,1,2,0 1,1,0,1,1, 3, î021, 3. i 20.3.0, 2, i, (a) (i) Find and s for this sample. (ii) Find E(X) and var(X) (iii) Find the method of moments estimate of θ iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the inaximum likelihood...
NOTE: DO Part b) ONLY
2. A discrete random variable X has the following pmf: A random sample of size n = 30 produced the following observations 1,3,0,00, 2, 22,0,1,2,0 1,1,0,1,1, 3, î021, 3. i 20.3.0, 2, i, (a) (i) Find and s for this sample. (ii) Find E(X) and var(X) (iii) Find the method of moments estimate of θ iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the inaximum likelihood...
(a) Below is the CDF for a discrete random variable, X if x 1 1/2 if 1 x< 2 if 2 x 3 7/8 if 3 x 4 F(x) = 3/4 2 1 if nx <n+1. Describe the probability 2n In general, note that for any positive integer n, F(x) distribution of X by finding P(X 1), P(X = 2), P(X positive integer n, and describe an experiment that would result in this random variable X. 3), and the general...
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