Question

need help for a and c. Thank you!

Two components of a laptop computer have the following joint probability density function for their useful lifetimes X and Y (in years): f(x,y) = a. Find the marginal probability density function of X, fx(x). Enter a formula below. Use for multiplication, / for division, A for power and exp for exponential function. For example, otherwise 3*xA3 exp(-x/3) means 3x3e3 X 2 0 Submit Answer Incorrect. Tries 3/10 Previous Tries b. Find the marginal probability density function of Y, M(y). Enter a formula below M)-1.6/(1 + 1.6*y)A2, y 20 You are correct. our receipt no. is 155-1262Previous Tries c. What is the probability that the lifetime of at least one component exceeds 1 year (when the manufacturer's warranty expires)? Round your answer to 4 decimal places. 0.6835 Submit Answer Incorrect. Tries 3/5 Previous Tries

Answer 1

a)marginal density of x: f(x)= $\int_{0}^{\infty }$ f(x,y) dy = $\int_{0}^{\infty }$ 1.6xe^-x(1+1.6y) dy =1.6xe^-x*(-e^-1.6xy/1.6x) | ^$\infty$ ₀ =e^-x

c)P(X u Y>1)=P(X>1)+P(Y>1)-P(X>1,Y>1)=0.36787944+0.3846153846-0.02856676 =0.7239