There are 3 blue and 5 green marbles in a box. Balls are selcted at random, one after another without replacement, until a green ball is selected. Let X be a random variable whose value is the number of balls drawn. Find the density function of X.

Since height is a continuous numerical variable, its probability density function is represented by the smooth curve below. What is true about the area under the curve? 140 160 180 200 height (cm) The area does not represent all possible heights, so the area under the curve and probability are both 0. O The area does not represent all possible heights, so the area above the curve is 1. O The area represents all possibile heights, so the area and probability are both 100. The area represents all possible heights, so the area under the curve and probability of all the height occurring are both 1.

Let x denote the lifetime (in thousands of hours) of a certain type of fan used in diesel engines. The density curve of x is as pictured below. 50 € (a) Shade the area under the curve corresponding to the probability that the lifetime is at least 25,000 hours. 0 00 24 25 24 50 (b) Shade the area under the curve corresponding to the probability that the lifetime exceeds 25,000 hours. 0 50 25 00 25 50 50 ⓇO⁰ 25 25 50 50 Ⓡ0⁰ Oo 26 26 50 50 C

Suppose we have a uniform density curve whose length is 2, what would the height of the density curve have to be? Write your answer in decimal form.