Show that area under multivariate normal distribution over the whole range in unity. Find characteristics function of multivaria
1 answer:
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Answer:
The gradient of is
.
Step-by-step explanation:
Geometrically speaking, the gradient of a curve is the slope of the tangent line at a given point of the curve. From perspective of Differential Calculus, the gradient is the first derivative of the curve. Let , then the gradient of the curve is:
(1)
The gradient of is
.
Answer:
a)
b)
c)
d)
e)
f)
g)
h)
Step-by-step explanation:
(a) F0.05, 4, 7 (Round your answer to two decimal places.)
For this case we need a valueof the F distribution with 4 degrees of freedom for the numerator and 7 for the denominator that accumulates 0.05 of the area on the left tail. We can use the following excel code: "=F.INV(0.05,4,7)". And we got:
(b) F0.05, 7, 4 (Round your answer to two decimal places.)
For this case we need a valueof the F distribution with 7 degrees of freedom for the numerator and 4 for the denominator that accumulates 0.05 of the area on the left tail. We can use the following excel code: "=F.INV(0.05,7,4)". And we got:
(c) F0.95, 4, 7 (Round your answer to three decimal places.)
For this case we need a valueof the F distribution with 4 degrees of freedom for the numerator and 7 for the denominator that accumulates 0.95 of the area on the left tail. We can use the following excel code: "=F.INV(0.95,4,7)". And we got:
(d) F0.95, 7, 4 (Round your answer to three decimal places.)
For this case we need a valueof the F distribution with 7 degrees of freedom for the numerator and 4 for the denominator that accumulates 0.95 of the area on the left tail. We can use the following excel code: "=F.INV(0.95,7,4)". And we got:
(e) the 99th percentile of the F distribution with v1 = 8, v2 = 12 (Round your answer to two decimal places.)
So for this case we need a value on the F distribution with 8 degrees of freedom for the numerator and 12 for the denominator that accumulates 0.99 of the area on the left tail. And we can use the following excel code: "=F.INV(0.99,8,12)". And we got:
(f) the 1st percentile of the F distribution with v1 = 8, v2 = 12 (Round your answer to three decimal places.)
So for this case we need a value on the F distribution with 8 degrees of freedom for the numerator and 12 for the denominator that accumulates 0.01 of the area on the left tail. And we can use the following excel code: "=F.INV(0.01,8,12)". And we got:
(g) P(F ≤ 6.26) for v1 = 5, v2 = 4 (Round your answer to two decimal places.)
For this case we want to find the probability that the F distribution with 5 degrees on the numerator and 4 on the denominator would be less or equal than 6.26. We can use the following excel code: "=F.DIST(6.26,5,4,TRUE)". And we got
(h) P(0.177 ≤ F ≤ 4.74) for v1 = 10, v2 = 5 (Round your answer to two decimal places.)
For this case we want to find the probability that the F distribution with 10 degrees on the numerator and 5 on the denominator would be between 0.177 and 4.74. We can use the following excel code: "=F.DIST(4.74,10,5,TRUE)-F.DIST(0.177,10,5,TRUE)". And we got
Answer:
23
Step-by-step explanation:
The median is the number in the middle of the data once it is organized from least to greatest, so that is what we must do first.
There are 19 numbers, that means that the 10th value will be the number in the middle
This means that the median is 23