If X, Y are correlated random variables, then E(X/Y) E(X):
a. True
b. False
If X and Y are uncorrelated RVs then they must be independent
a. True
b. False
The function f(x) = λe¯¹Âº¸ −∞ < x < ∞ a valid PDf
a. True
b. False
Given the function
fx(x)= 4 0 < x <b else
For the function to be vaild probability density, the constant b > 0
a. In2
b. In16
c. -In12 4
d. None of the above
Three statistically independent random variables X1, X2, X3 have mean (or ex- pected) values X1=3, X₂ = 6 X3 = -2. The mean value of g(X1, X2, X3) = -3X1X2-3X1X3 + 4X2X3 is
a. -84
b. -100
c. -90
d. 102
Random variable X and Y have the joint density
1 12 x y 4 3u(x)u(y) fxy(x, y) = ·e
The probability of the event {0 < x < ∞, Y < -1} is
a. 0.2349
b. 0.3168
c. 0.4946
d. None of these
A random variable X is uniformly distributed on the interval (-5, 15). Another X random variable Y = e 5 is formed. The value of E[Y] is:
a. 2
b. 0.667
c. 1.387
d. 2.967
The envelope of the output signal of a radar system that is receiving only noise is a random voltage X whose pdf is given by:
fx(x)=xe 2
The system gets a false target detection if X exceed a threshold level u volts. To make the probability of false detection 0.0001, then v>?
a. In1000 Volts
b. 2ln1000 Volts
c. Vln1000 Volts
d. √2ln10000 Volts
A joint sample space for two random variable X and Y has four elements (1, 1), (2, 2), (3, 3), (4, 4)
Probabilities of these elements are 0.1,0.35,0.05,0.5 respectively. The probability of the event {X<2, Y <6}
a. 0.45
b. 0.10
c. 0.55
d. 0.6
.