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10. (5pt) Suppose that X and Y are two normally distributed random variables. X has mean...
Please answer this question Suppose X is normally distributed with mean 1 and standard deviation 0.25,...
Please answer this question
Suppose X is normally distributed with mean 1 and standard
deviation 0.25, and Y...
Suppose X is normally distributed with mean 1 and standard deviation 0.25, and Y is also normal with mean 1.5 and standard deviation 0.4. Suppose that X and Y have correlation coefficient 0.6. Find the following probabilities: (a) P(X 2 1.3) (b) P(X+y-2.5) (c) P(X +Y 2 3) (d) P(Y - X so) (e) P(Y <X)
5. Suppose X is a normally distributed random variable with mean μ and variance 2. Consider...
5. Suppose X is a normally distributed random variable with mean μ and variance 2. Consider a new random variable, W=2X + 3. i. What is E(W)? ii. What is Var(W)? 6. Suppose the random variables X and Y are jointly distributed. Define a new random variable, W=2X+3Y. i. What is Var(W)? ii. What is Var(W) if X and Y are independent?
Question (c) Suppose you have two jointly distributed random variables, X and Y. Suppose you know...
Question (c) Suppose you have two jointly distributed random variables, X and Y. Suppose you know the following facts. • Var(–7.5 X) = 53.2925 • Var(1.5 x Y) = 1.01765 • Var(2 x X +3 + Y) = 6.26319 i. What is Cov(X,Y)? ii. What is the correlation of X and Y? iii. If you had a random sample of observations of x and y and estimated the regression Y = Bo + BiX +€ What would the
6. Consider a sample X,... X, of normally distributed random variables with mean y and variance...
6. Consider a sample X,... X, of normally distributed random variables with mean y and variance op. Let 5 be the sample variance and suppose that n = 16. What is the value of c for which p[x - SS (C2 - 1)] = 95 ? be the 7. Consider a sample X,...,X, of normally distributed random variables with variance o? = 30. Let S sample variance and suppose that n-61. What is the value of c for which P...
Suppose X and Y are random variables such that has a normal distribution with mean and...
Suppose X and Y are random variables such that has
a normal distribution with mean and
standard deviation ? = 1.
a). (4 points) Find a formula for E[Y |X = x].
b.) Compute E[Y]
fy(y|X = )
2. Consider the following two variables X and Y: 4 a. (2 pts) Find the mean of X, and mean of Y b...
please lease solve all
questions.
2. Consider the following two variables X and Y: 4 a. (2 pts) Find the mean of X, and mean of Y b. (2 pts) Find the standard deviation of X, and standard deviation of Y C. (3 pts) Find the covariance between X and Y d. (2 pts) Find correlation coefficient between X and Y and comment on your answer. 3. The following table shows a random sample of 100 hikers and the areas...
Suppose that the ages of PSU (undergraduate) students is independently and normally distributed witha mean of...
Suppose that the ages of PSU (undergraduate) students is independently and normally distributed witha mean of 19 and a standard deviation of 2. Suppose a first sample of four PSU students and a second sample of four PSU students are selected at random 1. What is the distribution of the sample mean, X, of the first four students? 2. What is the distribution of the sample mean, Y, of the other four students? 3. What is the distribution of 2X-Y?...
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined...
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x)-3 E(Y)9 E(Z)-2 Var(X) = 36 par(r)=19 par(Z)-10 Compute the values of the expressions below E (32 +3) 5Y+ 2x Var (5-2)-
Suppose X and Y are random variables such that fY (y|X = x) has a normal...
Suppose X and Y are random variables such that fY (y|X = x) has a normal distribution with mean µ = x/4 and standard deviation σ = 1. a). Find a formula for E[Y|X = x]. b). Compute E[Y ].
2. Suppose X is a normally distributed random variable with a mean of 85 and a...
2. Suppose X is a normally distributed random variable with a mean of 85 and a standard deviation of 5. Obtain the following probabilities. (a) P(80 < X < 86.5). [2 marks] (b) P(X> 76). [2 marks] (c) P(X< 87.8). [3 marks] (d) Find b such that P(X<b) = 0.7704 [3 marks]
Please answer this question
Suppose X is normally distributed with mean 1 and standard
deviation 0.25, and Y...
Suppose X is normally distributed with mean 1 and standard deviation 0.25, and Y is also normal with mean 1.5 and standard deviation 0.4. Suppose that X and Y have correlation coefficient 0.6. Find the following probabilities: (a) P(X 2 1.3) (b) P(X+y-2.5) (c) P(X +Y 2 3) (d) P(Y - X so) (e) P(Y <X)
Question (c) Suppose you have two jointly distributed random variables, X and Y. Suppose you know the following facts. • Var(–7.5 X) = 53.2925 • Var(1.5 x Y) = 1.01765 • Var(2 x X +3 + Y) = 6.26319 i. What is Cov(X,Y)? ii. What is the correlation of X and Y? iii. If you had a random sample of observations of x and y and estimated the regression Y = Bo + BiX +€ What would the
6. Consider a sample X,... X, of normally distributed random variables with mean y and variance op. Let 5 be the sample variance and suppose that n = 16. What is the value of c for which p[x - SS (C2 - 1)] = 95 ? be the 7. Consider a sample X,...,X, of normally distributed random variables with variance o? = 30. Let S sample variance and suppose that n-61. What is the value of c for which P...
Suppose X and Y are random variables such that has
a normal distribution with mean and
standard deviation ? = 1.
a). (4 points) Find a formula for E[Y |X = x].
b.) Compute E[Y]
fy(y|X = )
please lease solve all
questions.
2. Consider the following two variables X and Y: 4 a. (2 pts) Find the mean of X, and mean of Y b. (2 pts) Find the standard deviation of X, and standard deviation of Y C. (3 pts) Find the covariance between X and Y d. (2 pts) Find correlation coefficient between X and Y and comment on your answer. 3. The following table shows a random sample of 100 hikers and the areas...
Suppose that the ages of PSU (undergraduate) students is independently and normally distributed witha mean of 19 and a standard deviation of 2. Suppose a first sample of four PSU students and a second sample of four PSU students are selected at random 1. What is the distribution of the sample mean, X, of the first four students? 2. What is the distribution of the sample mean, Y, of the other four students? 3. What is the distribution of 2X-Y?...
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x)-3 E(Y)9 E(Z)-2 Var(X) = 36 par(r)=19 par(Z)-10 Compute the values of the expressions below E (32 +3) 5Y+ 2x Var (5-2)-
2. Suppose X is a normally distributed random variable with a mean of 85 and a standard deviation of 5. Obtain the following probabilities. (a) P(80 < X < 86.5). [2 marks] (b) P(X> 76). [2 marks] (c) P(X< 87.8). [3 marks] (d) Find b such that P(X<b) = 0.7704 [3 marks]
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