a) E(X), E(X²) and E[(X − 1)²] b) Var(X) and ox
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![Let X be a random variable having density function
f(x)
Sex x ≥ 0
to
Find
a) E(X), E (X²) and E[(X− 1)²]
b) Var (X) and ox
otherwise](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b55a0fb-5dff-4587-97c0-c3ec381e9c7e%2Fbd82d579-5b60-4ffc-bc16-f0ad4d0808a3%2Fy81d8sa_processed.png&w=3840&q=75)
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- Let f(x) is density function of continuous random variable x then the (expected value E(x Ek) = [ xfx)dx Ew) = [_fx)dx - 00 Ek) = ] -xfx)dx Ex)= | xf(x)dxLet Xbe a continuous random variable with density f (x) = 24x-4 for x > 2. Then Var (X) is equal to10) Let f(x) by the probability density function of some continuous random variable. Explain why it must be true that f(x) dx =1.
- The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by ´2e-(x+2) x 2 0, y 20 fx,y(x,y)=| else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.3935 b. 0.606 c. 0.7772 d. 0.3669 e. 0.6318Let (X, Y) be bivariate random variables having joint probability density function as f(x) = {;x +y) 0sx<2,0s ys2 otherwise Find the following: () The correlation coefficient between X and Y. (#)E(X"Y*)Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?
- Determine E(X), E(X2) and V(X) if X be a continuous random variable with probability density function fx(x) = 3x^2 0 ≤ x ≤ 1 0 otherwiseLet X be a random variable with pdf f(x) = kx*,-1The probability density of the random variable Z isgiven by f(z) = kze−z2for z > 00 for z F 0Find k and draw the graph of this probability density.2. Let X be a continuous random variable with probability density function (pdf) 3x�� 0Let X be a continuous random variable with probability density function f(x) = 2(1-x), 0<=x <= 1. If Y = 2X - 1, find the probability density function of Y. x is lower case X is upper case. I need to get upper case of YLet (X,Y) be bivariate random variables having joint probability density function as x) = ;(x + y) 0sx< 2,0 < y s 2 otherwise Find the following: (i) The correlation coefficient between X and Y. (ii)E (X"Y$)SEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,