please help me solve number 4

Page 0)

ZOOM (c) What is the most Sec 2 continuous random variable 4. 2.2.2 A random variable X takes values between 4 and 6 with a probability density function 1 xln(x) for 4 x 6 and f (x) = 0 elsewhere. (a) Make a sketch of the probability density function. (b) Check that the total area under the probability density function is equal to l. (c) What is P(4.5 X < 5.5)? (d) Construct and sketch the cumulative distribution function. (Hint: for (d), cumulative distribution function F(x) should be piece-wise function, F(x) are different on following interval : x 0)