Defn: A continuous r.v. X is said to have an F-distribution with m (numerator) and n (denominator) degrees of freedom (d.f.) if, and only if, the PDF of X is given by Notation: Mean : Variance: r(-) 士(帶)(③) w X-F(m.) E(X) = n n-2 m * Var(X) = DNE n>2 x(%)-1 (1+x)(0)(x), m.nez". 2n² (m+n-2) m(n-2)(n-4) n>4 Theorem: Let U-X) and V-X), with U and V independent. Then, MGF : Note: Prove F-distribution. Note: Use the proof of t-distribution as reference. X=-Fm %

Q: T+4 dx 620.18 %3D 2.

A: Given that: ∫25x5+4xdx

Q: 05- 2, Si

A: Given problem:- sincos-112 We have to find the value of the given expression.

Q: 103= 10%3D 2.

A: 102  = 100

Q: 2 +,

A:

Q: 3y = -x+6 %3D 2x + 4y = 12

A:

Q: 1+2x=77

A:

Q: 3×+5=23

A: this is a simple equation question  we will simplify by using the maths calculation rule.

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A: Adding Fractions Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add…

Q: 1 +1

A: Given  1+1=

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A: Given query is to find indicated limit.

Q: 3b-12 = 30

A:

Q: I need the answer as soon as possible

A: Solve the given problem.

Q: 4

A: Given equation 4-2x=40+5x Our aim is to find x value by solving the equation  For this we will do by…

Q: 2ex+1=8

A:

Q: -2/4x + 4 + 23 = 3

A:

Q: 11+2x=31

A:

Q: a = 2 - 9a

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Q: -3 1

A:

Q: 2х 5х- 2 X + 15 3

A: Explanation and solutions is given below....

Q: 2t2 – 100 = 0 %3D

A: The solution is, t = ±5√2  The detailed solution is as follows below:

Q: How do I find numbers 2 and 4?

A:

Q: 30 = 6 + z z =

A: Given : 30  = 6+z

Q: 43a+10-26a=27

A: To solve: 43a+10-26a=27

Q: 2X+3=9.X=

A: Solution

Q: カメ Z

A: Find value of  2+2x4

Q: Y+5>1

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: 4+b=30

A: It is addition and subtraction of numbers.

Q: 6z=36

A:

Q: c-4=9

A: Given equation 2c-4=9 we want to find the value of c

Q: -2/80 ->

A: Given: -2, ∠30