1.What is the expectation of Y~exp(1/lander) Is it E(X)=1/lander so the expectation in this case should...
1.What is the expectation of Y~exp(1/lander)
Is it E(X)=1/lander so the expectation in this case should be E(Y)=lander?????
2. What is the difference between poisson process and poisson distribution?
for the formula , i can tell that if the t=1,then the poisson processes is same as poisson distribution
Homework Answers
if
Y follows exp(1/lander)Add Answer to:
1.What is the expectation of Y~exp(1/lander)
Is it E(X)=1/lander so the expectation in this case should...
1. Let X and Y be two discrete random variables each with the same the possible...
1. Let X and Y be two discrete random variables each with the same the possible outcomes {1,2,3} a) Construct a bivariate probability mass function Px.y : {1,2,3} x {1,2,3} + R that satisfies the following properties propeties: (i) The expectation of X is E[X] = 2.1, (ii) The conditional expectation of Y given 2 = 3 is EY 2 = 3] = 1, (iii) The correlation between X and Y is slightly positive so that 0 < corr(X,Y) <...
Problem 4 (Conditional Expectation and Variance). Suppose the joint distri- bution of (X, Y) is given...
Problem 4 (Conditional Expectation and Variance). Suppose the joint distri- bution of (X, Y) is given by the following contingency (row represents x) table 20 points (x,y) 2 4 6 1 0.3 0 0.1 2 0 0.2 0 3 0.1 0 0.3 A) Compute the marginal distributions of X and Y B) Are X and Y independent? Explain. C) Find the conditional distribution of Y given X -1 D) Compute E[Y|X 1] E) Compute EY|X= 2] F Compute E[exp(X)Y|x 2
1. Consider the following distribution of (X Y) where X and Y ae both binary random...
1. Consider the following distribution of (X Y) where X and Y ae both binary random variables: 1/4 i (a)-(0.0 1/4 if (x, y) (0,0) 1/8 if (r,y) (1,0) Jx3/8 if (r,)- (0,1) ,Y (z, y) = 1/4 if (, ) (11 (a) What is the probability density function of Y? (b) What is the expectation of Y1 (c) What is the variance of Y? (d) What is the standard deviation of Y? (e) Do the same to X. (f)...
1. X,,x2,..., X, is a random sample from a Poisson (0) distribution with probability mass function...
1. X,,x2,..., X, is a random sample from a Poisson (0) distribution with probability mass function 0*e f(x) = x=0,1,..., 0 >0. x! (1) Write Poisson (0) as an exponential family of the form fo(x) = exp{c(0)T(x)-v (0)}h(x) State what c(0), 7(x), and y (@) are. (ii) a. Prove that for the exponential family given in (i), E[T(X)]=y'(c). b. Hence find the mean of the Poisson (0) distribution. [3] [6] [2] 21 (iii) Show that for the Poisson (0) distribution,...
Dealing with conditional probability and conditional expectation in these situa tions can be tricky, but we can always use a limiting process to work things out. For example, suppose we want E(X | Y...
Dealing with conditional probability and conditional expectation in these situa tions can be tricky, but we can always use a limiting process to work things out. For example, suppose we want E(X | Y = y, Z = z). We can figure this out by first computing pxiy,z (x | y, z), from which we obtain Use a limiting process to derive the (unintuitive to me, at least) formula Jylz(u|2)
Dealing with conditional probability and conditional expectation in these situa...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
what is the difference between poisson processes and poisson distribution? 1. Please explain the conception 2....
what is the difference between poisson processes and poisson distribution? 1. Please explain the conception 2. Please give me two example, one for poisson processes and one for poisson distribution. they can be a problem 3. please explain the difference between two examples. Follow the comment please
2. (10p) Consider two independent random variables X and . The first has a unform pdf on (o.2) and the latter a Poisson pmf with mean 3. (1) Find the correlation E[XY] 2) Find the expectation E[e...
2. (10p) Consider two independent random variables X and . The first has a unform pdf on (o.2) and the latter a Poisson pmf with mean 3. (1) Find the correlation E[XY] 2) Find the expectation E[e y'].
2. (10p) Consider two independent random variables X and . The first has a unform pdf on (o.2) and the latter a Poisson pmf with mean 3. (1) Find the correlation E[XY] 2) Find the expectation E[e y'].
Problem 1: x2 Expectation - The Hard Way The pdf of a x distribution is given...
Problem 1: x2 Expectation - The Hard Way The pdf of a x distribution is given by exp( 2 f (r|v) = 2ir We see that this is a special form of the Gamma distribution, with a v/2,B = 2. The general pdf of the Gamma distribution is written rlexp ( a-1 f(rla, B) = BaT(a) Part 1 Using properties of the pdf, show that exp(dA Br(a) Part 2 Using the fact proved above, compute the expected value of a...
Creat a matlab function that calculates: f(x, y) = xy/(exp(x) + exp(-y)) for two vectors of...
Creat a matlab function that calculates: f(x, y) = xy/(exp(x) + exp(-y)) for two vectors of values x and y. Name your function function_xy: The inputs should be in the same order: .X: vector of values • y: vector of values The ouput is: • A: is the calculated array f(x,y) Function 1 function (Outputs] = YourFunctionName(Inputs) 2 % Input code here end Code to call your function 1 X=-4:0.5:4 2 y=-5:1:5 4 A = function xy(x,y)
1. Let X and Y be two discrete random variables each with the same the possible outcomes {1,2,3} a) Construct a bivariate probability mass function Px.y : {1,2,3} x {1,2,3} + R that satisfies the following properties propeties: (i) The expectation of X is E[X] = 2.1, (ii) The conditional expectation of Y given 2 = 3 is EY 2 = 3] = 1, (iii) The correlation between X and Y is slightly positive so that 0 < corr(X,Y) <...
Problem 4 (Conditional Expectation and Variance). Suppose the joint distri- bution of (X, Y) is given by the following contingency (row represents x) table 20 points (x,y) 2 4 6 1 0.3 0 0.1 2 0 0.2 0 3 0.1 0 0.3 A) Compute the marginal distributions of X and Y B) Are X and Y independent? Explain. C) Find the conditional distribution of Y given X -1 D) Compute E[Y|X 1] E) Compute EY|X= 2] F Compute E[exp(X)Y|x 2
1. Consider the following distribution of (X Y) where X and Y ae both binary random variables: 1/4 i (a)-(0.0 1/4 if (x, y) (0,0) 1/8 if (r,y) (1,0) Jx3/8 if (r,)- (0,1) ,Y (z, y) = 1/4 if (, ) (11 (a) What is the probability density function of Y? (b) What is the expectation of Y1 (c) What is the variance of Y? (d) What is the standard deviation of Y? (e) Do the same to X. (f)...
1. X,,x2,..., X, is a random sample from a Poisson (0) distribution with probability mass function 0*e f(x) = x=0,1,..., 0 >0. x! (1) Write Poisson (0) as an exponential family of the form fo(x) = exp{c(0)T(x)-v (0)}h(x) State what c(0), 7(x), and y (@) are. (ii) a. Prove that for the exponential family given in (i), E[T(X)]=y'(c). b. Hence find the mean of the Poisson (0) distribution. [3] [6] [2] 21 (iii) Show that for the Poisson (0) distribution,...
Dealing with conditional probability and conditional expectation in these situa tions can be tricky, but we can always use a limiting process to work things out. For example, suppose we want E(X | Y = y, Z = z). We can figure this out by first computing pxiy,z (x | y, z), from which we obtain Use a limiting process to derive the (unintuitive to me, at least) formula Jylz(u|2)
Dealing with conditional probability and conditional expectation in these situa...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
2. (10p) Consider two independent random variables X and . The first has a unform pdf on (o.2) and the latter a Poisson pmf with mean 3. (1) Find the correlation E[XY] 2) Find the expectation E[e y'].
2. (10p) Consider two independent random variables X and . The first has a unform pdf on (o.2) and the latter a Poisson pmf with mean 3. (1) Find the correlation E[XY] 2) Find the expectation E[e y'].
Problem 1: x2 Expectation - The Hard Way The pdf of a x distribution is given by exp( 2 f (r|v) = 2ir We see that this is a special form of the Gamma distribution, with a v/2,B = 2. The general pdf of the Gamma distribution is written rlexp ( a-1 f(rla, B) = BaT(a) Part 1 Using properties of the pdf, show that exp(dA Br(a) Part 2 Using the fact proved above, compute the expected value of a...
Creat a matlab function that calculates: f(x, y) = xy/(exp(x) + exp(-y)) for two vectors of values x and y. Name your function function_xy: The inputs should be in the same order: .X: vector of values • y: vector of values The ouput is: • A: is the calculated array f(x,y) Function 1 function (Outputs] = YourFunctionName(Inputs) 2 % Input code here end Code to call your function 1 X=-4:0.5:4 2 y=-5:1:5 4 A = function xy(x,y)
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