For this exercise, give exact answers as simplified fractions. Compute E (X) and Var(X) if X has probability density function given by . . .
1)for this to be valid:
f(x)dx =
c*(1-x6) dx =c*(x-x7/7) |1-1
=c*12/7=1
c=7/12
2)
E(X)=
xf(x)dx =
(7/12)*(x-x7) dx =c*(x2/2-x8/8)
|1-1 =0
E(X2) =
x2f(x)dx =
(7/12)*(x2-x8) dx
=c*(x3/3-x9/9)
|1-1=7/27
therefore Var(X)=E(X2)-(E(X))2 =7/27-02=7/27
For this exercise, give exact answers as simplified fractions. Compute E (X) and Var(X) if X...
For this exercise, give exact answers as simplified fractions. Compute E (X) and Var (X) if X has probability density function given by ... c(1-26) if –1<<1 a) fx(r) = 10 otherwise Determine the value of cas part of your answer. c/ if b) fx(x) = > 5 10 otherwise Determine the value of cas part of your answer. Hint: The variance does not necessarily need to be finite.
EXERCISE (x2+1), where . < 1) A random variable X has the density function f(x)= a) Find the value of the constant C b) Find the probability that X lies between 1/3 and 1
The random variable X has the probability density function (x)a +br20 otherwise If E(X) 0.6, find (a) P(X <름) (b) Var(x)
Obtain E(Z|X), Var(Z|X) and verify that E(E(Z|X)) =E(Z),
Var(E(Z|X))+E(Var(Z|X)) =Var(Z)
3. Let X, Y be independent Exponential (1) random variables. Define 1, if X Y<2 Obtain E (Z|X), Var(ZX) and verify that E(E(Zx)) E(Z), Var(E(Z|X))+E(Var(Z|X)) - Var(Z)
TT α Given that cosa = 3 4 and 0 <« <z, determine the exact value of cos z α COSE cos 2 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression
2.6.17. The probability density function of the random variable X is given by r2 21 0<x-1, 6x-2r2-3 (x, 3)2 0 otherwise.
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
Problem 29.1 Let X have the density function given by 0.2 -1<r<0 f(x) = 0.2 + cx 0 〈 x < 1 otherwise. (a) Find the value of c.
1. Two normal random variables X and Y are jointly distributed with Var(X) 25 and Var(Y) 1600. It is known that P(Y>80| X = 50) 0.1 and P(Y 22 X 40) 0.7886 (1) What is the correlation coefficient between X and Y? (2) What is the expected value of Y given X 50?
The answers for part b are sin(A/2) = √26/26, cos(A/2) =
-5√26/26, and tan(A/2) = -1/5, but I can't figure out how to get
there
lies and (b) find the 24. Iftan A = with 34 < A< 21, then (a) determine the quadrant in which exact value of sin (), cos (), and tan ().