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Concept explainers
C In Problems 17–20, use a graphing calculator to graph the normal probability density function
that has the given mean μ and standard deviation σ.
17. μ = 0, σ = 1
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Chapter 6 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
- 4. "Time headway" In highway traffic flow the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point is called time headway. Now, let X = the time headway for two randomly chosen consecutive cars on a highway during a period of heavy traffic flow. The following probability density function of X is suggested by traffic experts: f(x) = 0.15*e-0.15(x-0.5) for (x ≥ 0.5 sec) 0 otherwise a. Draw f(x) from x = 0 to x= 10 sec. b. Find P(X ≤ 5 sec) and show it on the figure you have drawn. c. What is E[X] and Var[X] ? d. Find Cumulative Distribution Function of X.arrow_forwardSuppose that the random variable X has the probability density function f(x) = {" c(1- x2) for - 1s x s1 elsewhere What is the variance of X A 1/2 B 1/3 1/5 D 1/4arrow_forward11. The distribution function of a random variable X is given by -e-x² X>0 otherwise F(x)= Find the probability density function.arrow_forward
- Situation 9. Suppose that X has a lognormal distribution with parameters 0 = -2 and ² = 9. Determine the following: 18. P(500 x) = 0.1 20. The variance of X.arrow_forwardQ.7 For an exponential distribution fx(x; 4) = {4e*; Sue Hx, x 2 0 e.w. where u > 0 Write (Don't derive) (a) Mean (expected value), i.e. EX). (b) Standard deviation, i.e. S. D. (X). (c) Moment generating function, i.e. Mx(t). (d) Cumulative distribution function (cdf), Fx(x). of Nizyarrow_forwardQ.1 Let X is the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has probability mass function X 13.5 15.9 19.1 P(X = x) 0.2 0.5 0.3 %3D (i) Verify that it is a probability mass function. (ii) Find mean and standard deviation of above probability mass function. (iii) Find the probability that X is atleast 15. (iv) If the price of a freezer having capacity X cubic feet is 25X – 8.5, what is the expected price and variance paid by the next customer to buy a freezer? (v) Find moment generating function.arrow_forward
- 2. If the random variable X has the probability density function f(x) = (1-x²), -1 < x < 1, 3 4 what is the variance of 15X + 2?arrow_forward22. If the random variable X - Exp(0), then what is the probability density function of the random variable Y = XVX?arrow_forward19. In Saint Tropez, the probability that it rains on a given day is 10%. Given that it rains, the amount of rain has a density of f(x) = (1/3)e-/3. Find the variance of the amount of rain on a given day. A. 0.9 B. 1.7 C. 3.0 E. 9.0 D. 4.4arrow_forward
- Q.7 For an exponential distribution fx(x; 4) = (ue Hx: x 20 %3D where u > 0 Write (Don't derive) (a) Mean (expected value), i.e. E(X). (b) Standard deviation, i.e. S.D. (X). (c) Moment generating function, i.e. Mx(t). (d) Cumulative distribution function (cdf), Fx(x). of Nizwarrow_forwardProb. 3 Let X be a random variable with cumulative distribution function (cdf) given by (1-e-x², x ≥ 0 ={1,- x<0 Find the probability that the random variable X falls within one standard deviation of its mean. Fx (x) =arrow_forward3. (a) A random variable, X, has the following probability density function: for 0 S<2 S(m) = (20 - 42)/30 for 2 S S6 otherwise. 1. Sketch the graph of f(#). (The sketch can be drawn on ordinary paper graph paper needed.) -no il. Derive the cumulative distribution function of X. ill. Find the mean and the standard deviation of X.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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