. Let x and y be joint continuous random variable with joint pdf (сх + 1, 0, x, y 2 0, x + y < 1 otherwise f XY (х, у) 1. Find the constant c. 2. Find the marginal PDF'S fx (x) and fy (y) 3. Find P(Y<2X²)

a) You throw two fair dice labeled 1, . . . , 6 independently of each other and let X be the minimum of the two results. Calculate E[X2]. (b) Suppose that X has pdf given by f(x) = 3x^(−4) if x > 1 and by f(x) = 0 if x <= 1. Calculate the median of X.

Suppose X has PDF fX (x) = 4x(1 − x^2) for 0 < x < 1 (0 everywhere else). Find all mediansand modes for X.(a)  Find all medians of X.(b)  Find all modes of X.

Calculate correlation and probable error between physical parameters (temperature and humidity) Number of families(x)=2 Number of sites(n)= 1 Temperature(y) in autumn= 24.1 Humidity(y) in autumn= 35 20 1 19 Calculate correlation and probable error between physical parameters (temperature and humidity) Using the following formula coefficient of correlation (r). r = n([xy)-([x) (Ey) V[n(Ex 2)-(Ex) 2][n(Ey2)-([y) 2] I