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• ### -/1 points 1. ASWESBE9 6.E.033. Consider the following exponential probability density function. f(x) e-x/5 5 1 for x 0... -/1 points 1. ASWESBE9 6.E.033. Consider the following exponential probability density function. f(x) e-x/5 5 1 for x 0 (a) Write the formula for P(x s xn) (b) Find P(x s 2). (Round your answer to four decimal places.) (c) Find P(x z 5). (Round your answer to four decimal places.) (d) Find P(x s 6). (Round your answer to four decimal places.) (e) Find P(2 s x s 6). (Round your answer to four decimal places.) Need Help? Read...

• ### Consider the following exponential probability density function. f(x) = 1 4 e−x/4 &n...

Consider the following exponential probability density function. f(x) = 1 4 e−x/4     for x ≥ 0 (a) Write the formula for P(x ≤ x0).    (b) Find P(x ≤ 3). (Round your answer to four decimal places.) (c) Find P(x ≥ 4). (Round your answer to four decimal places.) (d) Find P(x ≤ 6). (Round your answer to four decimal places.) (e) Find P(3 ≤ x ≤ 6). (Round your answer to four decimal places.)

• ### Consider the following exponential probability density function.  for x ≥ 0 If needed, round your answer...

Consider the following exponential probability density function.  for x ≥ 0 If needed, round your answer to four decimal digits. (a) Choose the correct formula for P(x ≤ x0). (i) (ii) (iii) (iv) (b) Find P(x ≤ 2). (c) Find P(x ≥ 3). (d) Find P(x ≤ 5). (e) Find P(2 ≤ x ≤ 5).

• ### Exercise 10.2 (Algorithmic)) Consider the following hypothesis test. Hai μι-μ2 > 0 The following results are... Exercise 10.2 (Algorithmic)) Consider the following hypothesis test. Hai μι-μ2 > 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1- 30 n 2 70 X1=25.9 X2=22.7 01 5.7 ơZE 7 a. What is the value of the test statistic (round to 2 decimals)? b. What is the p-value (round to 4 decimals)? Use z-value rounded to 2 decimal places.

• ### 3. Let X be a continuous random variable with probability density function ax2 + bx f(0)... 3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...

• ### 5. The Exponential(A) distribution has density f(x) = for x<0' where λ > 0 (a) Show/of(x)... 5. The Exponential(A) distribution has density f(x) = for x<0' where λ > 0 (a) Show/of(x) dr-1. (b) Find F(x). Of course there is a separate answer for x 2 0 and x <0 (c Let X have an exponential density with parameter λ > 0 Prove the 'Inemoryless" property: P(X > t + s|X > s) = P(X > t) for t > 0 and s > 0. For example, the probability that the conversation lasts at least t...

• ### A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density... A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).

• ### 2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise.... 2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)

• ### Find the median of exponential distribution with probability density function f(x) = * e * P... Find the median of exponential distribution with probability density function f(x) = * e * P -2

• ### Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5... Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).