Suppose X and Y have joint probability density function 1/2 if 0 < x < 1, 0 < y < 1, 1/3 if 1
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- Show that each function defined as follows is a probability density function on the given interval; then the indicated probabilities. f(x)=12(1+x)3/2;[0,) a. P(0X2) b. P(1X3) c. P(X5)Show that each function defined as follows is a probability density function on the given interval; then find the indicated probabilities. f(x)=(1/2)ex/2;[0,) a. P(0X1) b. P(1X3) c. P(X2)