following p. def.: Consider continuous r... X w/ the -X $(x) = otherwise Ta Find E(X)....
0 Consider continuous r. V. X w the following p. def.: $(x) = for os x 3 o otherwise a Find E(X). 5 Find Pla=X=4).
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1
-l 2. Consider the continuous-time signal: 0 x(t)- 1sts1 0, otherwise Find the Fourier transform X(a) of x(t). Simplify ths expression as much as po e simplest expression does not involve any complex numbers.) Draw a rough plot of o) as a function of w. Identify the peak value of X(w). Identify the location of the X( first null on either side of the vertical axis.
13. The random variables X,Y are jointly continuous with the jpdf 0 otherwise (a) Find P(2Y>X). (b) Find the conditional expectation E(XY -0.5).
Problem(2) (5 points) A continuous distribution has density function k sin(r); 0rST 0; f(x) = otherwise. (a) Find the numerical value of k so that f(r) is a density function. (b) Find E[X] (c) Find E[X2. (d) Find Var X] Problem(2) (5 points) A continuous distribution has density function k sin(r); 0rST 0; f(x) = otherwise. (a) Find the numerical value of k so that f(r) is a density function. (b) Find E[X] (c) Find E[X2. (d) Find Var X]
X with density fcx)3/56 ir 2<<4 5. Consider a continuous random variable X with density f(x)- otherwise a. Find P(1 <X<3) b. Find ECX)
Real analysis 2. Consider the following three definitions: A function f : R-+R is lax-continuous at a E R provided for all e > 0 there is a 6 > 0 such that for all r E R, if x - al6 then |f(x)- f (a)e A function f : R - R is e-continuous at a E R provided for all e >0 there is a 6 > 0 such that for all r E R, if |a- a...
Consider the following function: def w(x, y) : z = x + y return z What is the function's name? Group of answer choices w x y z
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1, f() = 0. Otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(2) of X. (c) Use F(2) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
X and Y are jointly continuous with joint pdf fa,y) - Otherwise Find c. b. Find P(X Y <1). c. | Find marginal pdrs of X and of Y. . Are X and Y independent? Justify. 2 pt. 2 p 2 pt. 2 pt. /cof, sto , 24