Pulses arrive at a counter according to a Poisson distribution having an average = 2 pulses per minute. Let X denote the number of pulses arriving during a 5 minute interval. P[9 < X < 11] is:

EXAMPLE 6.39 If cu = 4/5 in an (M/M/c): (/FCFS) queueing system, find the average number of customers in the non-empty queue.

I need help with parts “c”, “d, and “e” thanks.

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9. If the moment generating function of X is M(1) = 2 find the mean, variance and p.d.f. of X.

5. A group of doctors are conducting a clinical trial for an experimental cancer drug. The graph below shows the probability of patient survival as a function of time, t (in months). The functions for Streated (survival probability of patients treated by the drug) and Splacebo (survival probability of patients given a placebo) are determined to be: Streated(t) = e-() and Splacebo (t) = e #. Use the given function (a) Splacebo (t) = e-i to calculate the average survival probability of the placebo group for the first 10 months of the study. Round to 2 decimal places. Ste 0. -0.6 -0:4 -02 10 20 (b) The efficacy of the drug at any time 7 >0 can be defined as E(7) = (Streated(t) – Splacebo (t)) dt. Note: This can be thought of as representing a difference of areas. Use a Riemann sum with 5 sub-intervals of equal width to approximate E(10). Use right endpoints. Round your final answer to 2 decimal places. (c) the first 7 months). Is the drug beneficial at 10 months? (A short one-sentence…

5. A group of doctors are conducting a clinical trial for an experimental cancer drug. The graph below shows the probability of patient survival as a function of time, t (in months). The functions for Streated (survival probability of patients treated by the drug) and Splacebo (survival probability of patients given a placebo) are determined to be: Streated(t) = e-(15)" and Splacebo (t) = e 15t 144. (a) "Ise the given function 15t Ppiacevo \" e-144 to calculate %3D Spreated the average survival probability of the placebo group for the first 10 months of the study. Round to 2 decimal places. 5-0:8 -0:6 Splacebo -0:4 0:2 10 20 (b) The efficacy of the drug at any timer > 0 can be defined as E(T) = | (Streated(t) – Splacebo (t)) dt. Note: This can be thought of as representing a difference of areas. Use a Riemann sum with 5 sub-intervals of equal width to approximate E(10). Use right endpoints. Round your final answer to 2 decimal places. (c) the first T months). Is the drug beneficial at…

Suppose 1.8% of every Filipino births result in twins. From a random sample of 1000 births, let X be the number of twins. That is X = {0, 1, 2, ..., 1000). Find the E(X).

7. Suppose the distribution of waiting times (in hours) for residents of a particular province trying to book a vaccination appointment is determined by the function 5 5t f (t) ==e¯6, t >0 Find the percentage of residents who wait longer than the mean waiting time. In a sample of 1250 residents, we expect that the number of residents who wait longer than the median waiting time will be