Consider the pdf g(y) = .06(y² + 1) on -2 ≤ y ≤ 3. (a) Calculate the probability that P(Y > 1). (b) Calculate E[Y]. (c) Calculate Var(Y).

Q: P(z > c) = 0.6126

A: Let z be the standard normal variable with mean μ=0 and standard deviation σ=1 The value of c is,

Q: integrate x/(1 + |x|) dx from - 3 to 3

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Q: Let F(x) = x² + 7 and G(x) = vx + 8 Evaluate: (a) (G o F) (x) (b) (G o F)(3) (c) (F o G)(1) (d) (F…

A: We need to find composition of functions

Q: (d) Find the average rate of change of f(x) in the interval [-4,6].

A:

Q: Let h(x) = 3x² + x -x² + 3x - 3 what is h' (2)?

A: We need to find out h'(2).

Q: y fG) = 16 %3D (0.25e-0.5(y-4) b. i) Find Pr(3 <YS 5), correct to four decimal pla

A:

Q: LetP(B) = 0.6, P(K|B) = 0.2, P(K|B') = 0.35. FIND THE VALUE OF P(K)

A: P(B)=0.6P(K|B)=0.2P(K|B')=0.35

Q: Find a power series for each of the following, centered at a = 0 for parts (a) - (d) and centered at…

A: The function f(x)  is a rule that associates or fixes a number to the particular point x. Derivative…

Q: Differentiate the function. c² – z² c2 + z? H(z) = In

A:

Q: 3 f(x) dx = 4, find | xf(x*) dx. If f is continuous and

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Q: Let F(x) =Cx41D, fCx)=X,and gox)=x+1 True or fals e (gof)(x) = FCX).

A:

Q: P(ze <z < 0)=0.390

A: From the provided information, P (ze &lt; z &lt; 0) = 0.390

Q: P(A | B) = 0.1, P(B) = 0.7, P(A | B') = 0.4. Find P(B | A).

A:

Q: (f) P(Z > z* or z <-z*) = 0.2044 * z* = -2.48

A: P(z &gt; z* or z &lt; -z*) = 0.2044

Q: Suppose X and Y have the following joint PMF. æ\y_ 1 2 3 4 1/6 1/6 0 1 1/12 1/12 0 1/12 1/12 0 1/6 0…

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Q: Consider the PDF f(x) = (1/2)(x+1), -1<x<1 Find the PDF for Y = 1-|X|

A: Probability Theory:Understand the concept of probability, random variables, and probability…

Q: 2 + Vx dx. (a) Evaluate 1 dx. x + x(ln x)2 (b) Evaluate

A: Explained below

Q: 9a) Find the local extrema of the function f(x) = e*(x² -3) using the Second Derivative Test.

A: