Problem 1 Let X be a continuous random variable uniformly distributed over [c, d], and let Y = aX+b, where a and b are any constants. Find the cumulative distribution function Fy (y) and the density function fy (y). (Hint: Remember to consider all possible values for a and y.)

Q: 2/18 – 12/32 + 3V50

A: The solution is given below in the next step:

Q: 4 2 G F -8 -4 -2 2 10 -2 -4 E 10 K 00

A: Formula for area is length multiply by breadth. Similarly for square its a^2 if side of square is…

Q: -5 dx Evaluate 2x 10 A B c) 1 (D) 2

A: formula:

Q: 30 Evaluate (1 + i)

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Q: 4 Evaluate -1 0 5 by: 3 - 2 expanding along the first row expanding along the second column A A 1.…

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Q: Prove that X Pn dx %3D

A: Recurrence relation.  Partial fraction.

Q: 10 8/10 + 9 7/12=

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Q: 100 Find the coefficient of x10 in the expansion of (2x +;

A: To find the coefficient of x10 in the expansion of 2x+1x100 we will use(r+1)th term in the expansion…

Q: 4n – 1

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Q: 1 1 dx 3 5 x +x4

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Q: Find the coefficient of x5in the expansion of (1 – 2x + 3x2)5

A: I have solved Algebraically

Q: 9 – 4x > –3

A: The given inequality is 9-4x>-3

Q: Write the binomial expansion for (x + 2)°. (x+ 2)° =D

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Q: 3 dx 9

A: The given integral is: I=∫x3x2-9dx

Q: Find the coefficient of x4 in the expansion of (2-3x)6

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Q: 50/21 simplest form

A: Compute the simplest form of 50/21.That is, divide 50 by 21.

Q: Find the 7th and 11th term of the expansion (y − x)^14

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Q: 1 3] [1 3 3 0 -1 2. 30 2

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Q: Find a if the 17th and 18th terms of the expansion (2 + a)5⁰ are equal.

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Q: find the slopet y-intercept the line 2.

A: Given equation of line is  2x+3y=24

Q: Write the first, third and fifth terms of the expansion of (3x – 5y)5.

A: Write the first ,third and fifth term of the expansion of (3x-5y)5.

Q: expansion of (1-2m)“

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Q: ext dx 8X-X

A: We have to evaluate the ∫dx8x-x2

Q: 36 70

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Q: In the expansion of (x + 4/x)12, find the term without x. a. 63 360 C. 506 880 b. 126 720 d. 3 784…

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Q: Find the coefficient of x8 y18  in the expansion of (1x2  -4y6)7

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Q: 22 7/8 - 7=

A: Given,

Q: Write the binomial expansion of (2x – 1) as a polynomial in simplest form.

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Q: 1/20+1/10+1/4

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Q: efind the intergrationa

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Q: 3 S x²_9

A: