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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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- 6. Consider an Exponential Distribution with parameter m = 0.2 A. Write the Probability Density function f(x) for this Distribution B. Write the Cumulative Density function F(x) for this Distribution C. What are the Mean and Standard Deviation of this Probability Density Functionarrow_forward3. (a) A random variable, X, has the following probability density function: for 0 S <2 S (m) = { (20 - 4æ)/30 for 2 S6 0. otherwise. 1 Sketch the graph of f(2). (The sketch can be drawn on ordinary paper- no graph paper needed.) II. Derive the cumulative distribution function of X. iil. Find the mean and the standard deviation 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_forward
- 11. The distribution function of a random variable X is given by -e-x² X>0 otherwise F(x)= Find the probability density function.arrow_forward2. 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_forwardSituation 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_forward
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- 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_forward5. Assume = 0.06 and let the force of mortality be given by 0.04, 0 < t < 20 { 0.05, 20arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,