Question

X: 3,4,5,7,8

Y:3,7,6,12,13

Find beta 0 and beta 1

Compute standard error

Compute Sb1

Compute p value

Answer #1

From the given data,

Price (X) | Score Y) | X^2 | Y^2 | XY | |

3 | 3 | 9 | 9 | 9 | |

4 | 7 | 16 | 49 | 28 | |

5 | 6 | 25 | 36 | 30 | |

7 | 12 | 49 | 144 | 84 | |

8 | 13 | 64 | 169 | 104 | |

Total: | 27 | 41 | 163 | 407 | 255 |

Let Y ⇠ Gamma(alpha,beta) and conditioned on Y = y, X
⇠ Poisson(y).
Find the unconditional distribution of X in the case that alpha = r
is an integer and beta=1-p/p
for p in (0, 1).
Find the conditional
distribution of Y|X = x. (Use Bayes’ rule)

GIVEN INFORMATION
{X=0, Y=0} = 36 {X=0, Y=1} = 4 {X=1, Y=0} = 4 {X=1, Y=1} = 6
1. Use observed cell counts found in the given information to
estimate the joint probabilities for (X = x, Y = y)
2. Find the marginal probabilities of X = x and Y = y
3. Find P (Y = 1|X = 1) and P (Y = 1|X = 0)
4. Find P (X = 1 ∪ Y = 1)
5. Use...

Suppose f(x,y)=(1/8)(6-x-y) for 0<x<2 and 2<y<4.
Find p(0.5 < X < 1) and p(2 < Y < 3)
Find p(Y<3|X=1)
Find p(Y<3|0.5<X<1)

Let X and Y be random variables, P(X = −1) = P(X = 0) = P(X = 1)
= 1/3 and Y take the value 1 if X = 0 and 0 otherwise. Find the
covariance and check if random variables are independent.
How to check if they are independent since it does not mean that
if the covariance is zero then the variables must be
independent.

Consider the following joint distribution between random
variables X and Y:
Y=0
Y=1
Y=2
X=0
P(X=0, Y=0) = 5/20
P(X=0, Y=1) =3/20
P(X=0, Y=2) = 1/20
X=1
P(X=1, Y=0) = 3/20
P(X=1, Y=1) = 4/20
P(X=1, Y=2) = 4/20
Further, E[X] = 0.55, E[Y] = 0.85, Var[X] = 0.2475 and Var[Y] =
0.6275.
a. (6 points) Find the covariance between X and Y.
b. (6 points) Find E[X | Y = 0].
c. (6 points) Are X and Y independent?...

For the data set shown below, complete parts (a) through (d)
below.
X 20 30 40 50 60 Y 98 93 91 85 68
(a) Use technology to find the estimates of beta 0 and beta
1.
beta 0 ~ b 0=_____(Round to two decimal places as needed.)
beta 1 ~ b 1=_____(Round to two decimal places as needed.)
(b) Use technology to compute the standard error, the point
estimate for o' (o with a little tag on the...

Suppose that(X,Y)is uniformly distributed over the rectangular
region with corners(0, 0),(2, 0),(2, 1),(0, 1).
Compute the following:
(1)P{X=Y}
(2)P{X < Y}
(3)P{X < Y^2}

X Y 1 50 8 57 11 43 16 18 20 18 Use the estimated regression
equation is y = 61.5 – 2.21x. A). Compute the Mean Square Error
Using Equation. S^2 = MSE = SSE/(n-2) B). Compute The Standard
Error of the estimate using equation. S = SQRT(MSE) =
SQRT[SSE/(n-2)] C). Compute the estimated Standard Deviation of b1
using equation. Sb1 = S/SQRT[SUM(x-(x-bar))^2] D). Use the t-test
to test the following hypothesis (α = 0.05) H0: β1 = 0...

Given : f(x,y)=6x, 0<x<1,0<y<1−x
Find: marginal pdf’s for X and Y, conditional pdf’s, P(0 < X
< 0.5,0 < Y < 0.25), E(X), and V(X)

Consider
f(x, y) = (x ^2)y + 3xy − x(y^2)
and point P (1, 0).
Find the directional derivative of f at P in the direction of ⃗v
= 〈1, 1〉. Starting from P , in what direction does f have the
maximal rate of change? Calculate the maximal rate of change

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