Example: Given the joint probability density function f(x,y) = 3x. 0
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Q: 4: 1) If the E(XY) = 5 and the mean of X and Y are both equal to 3, then what is the covariance of…
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A: Scatter Diagram (i) insert →scatter plot
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- A lamp has a lightbulb with an average lifetime of 4 hours. The probability density function for the lifetime of a bulb is f(t)=14e−t/4,t≥0.What is the probability that the bulb will fail within 5 hours?If Θ ∼ Uniform(a = 0, b = 3), find the probability density function of sin(Θ).2. Identify the probability density function, then find the mean and variance without integrating. b. f(x) =1/6 e^−x/6, [0,∞) c. f(x) =1 / 3√2π e^−(x−16)^2/18, (−∞,∞)
- A continuous variable Y has a probability density function for which the moment generating function is given by M(t)=e^(2*t+72*t^2). What is the variance of the variable, Var[Y]?The length of time for students to complete a 1-hour timed standardized mathematics test has a probability density function f(t) = 1.5t2 + t, 0 ≤ t ≤ 1Suppose that the unknown X is ≥ 2 and has the probability density function fX(x)=Ce^−x,x ≥ 2.What is the numerical value of C?
- The joint probability density function of X and Y is: f(x,y)={ k(x+y) if 0≤x≤1 and 0≤y≤1 0 otherwise. a) What is P(X < Y)? b) What is E(X)? c) What is E(2Y)?Calculate the E(X) when the joint probability density function of X and Y is fxy(X,Y)=c(X+Y) over the range x = 1, ..., 4 and y = 1, ..., 2The joint probability density function of X and Y is given byf(x,y) = x+y 0 < x < 1, 0 < y < 1 (d) E(xy) = ? (e) Cov(x,y) = ?