Problem 3. (16 points) Let ¢ be a point selected at random uniformly from the unit interval [0,1]. Consider the random variable X = es. (a) (b) ts) Sketch X as a function of C. Find and plot the CDF of X. (c) Find the probability of the events {X > √e} and {e0.25 < X ≤ e0.75}.

When a man observed a sobriety checkpoint conducted by a police​ department, he saw 656 drivers were screened and 5 were arrested for driving while intoxicated. Based on those​ results, we can estimate that P(W)equals=0.00762​,where W denotes the event of screening a driver and getting someone who is intoxicated. What does P(W) ​denote, and what is its​ value? What does P(W) ​represent? P(W)=

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X P(x) =C p*q"-x %3D When processing credit-card applications there is a 40% chance that an application will have incomplete or insufficient information and require research. You have 5 applications in your to-do pile and would like to leave early today. (a) Fill in the values: n = q = (b) What is the probability of exactly three applications needing research? (enter a number between 0 and 1, 4 decimal places) Answer= (c) What is the expected number of applications that will need research? Answer= (d) What is the probability of having AT LEAST the expected number of applications needing research? (enter a number between 0 and 1, 4 decimal places) Answer= Please answer all parts of the question.

Suppose Xt denotes the unknown whose value is the success count for ?ttrials of a Bernoulli Process with success rate p and Wn the unknown whose value is the number of trials to have the nth success.  Then, the probability that the number of trials to get the 7th success is at most 10 is which of the following? (A)  P(X10≥7)P(X10≥7) (B)  P(X7<10)P(X7<10) (C)  P(X10<7)P(X10<7) (D)  P(W7≥10)