Question

Q: Asking for assistance in understanding and solving this example on Probability and Statistical with the steps of the solution to better understand, thanks.

**Please give the step by steps with details to completely see how the solution came about.

1) The joint pmf of X and Y is given by: f(x,y) = c(x+1)(4-x)(y+1)(3-y), x=0,1,2,3 y=0,1,2 with y $\leq$ x.

    (a) Find the value of c.

    (b) Sketch the support of X and Y.

    (c) Record the marginal pmfs f_x(x) and f_y(y) in the 'margins.

    (d) Are X and Y independent?

    (e) Compute $\mu$ _x and $\sigma$ ²x.

    (f) Compute $\mu$ _y and $\sigma$ ²y.

    (g) Compute Cov(X,Y).

    (h) Determine $\rho$ , the correlation coefficient.

    (i) Find the best-fitting line and draw it on your figure.

Answer 1

2. y=f, y=z, when , 2, 3 when χ=2,3 15 b) 2 42 1sy 154 154 75y

2- a). XndY ane not independeat bucause So the value, of y depends on χ is y 15ч is y 154 Is 4