Now that you know how how the commands qnorm and pnorm work, compute the following items a to d below for a random variable X ~ N(10, 16):(a) P(X < 2)(b) P(X > 18)(c) Value x such that P(X < x) = 0.05(d) Value x such that P(X > x) = 0.95(a)(b)(c)(d)

To compute the probabilities and quantiles for a normal random variable X ~ N(10, 16), we can use…

Answered: Now that you know how how the commands…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of heads in each outcome. For example, if the outcome is tth, then =Rtth1. Suppose that the random variable X is defined in terms of R as follows: =X−R2−3R4. The values of X are given in the table below. Outcome htt tht hth thh ttt hhh hht tth Value of X −6 −6 −6 −6 −4 −4 −6 −6 Calculate the values of the probability distribution function of X, i.e. the function p X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.

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Now that you know how how the commands qnorm and pnorm work, compute the following items a to d below for a random variable X ~ N(10, 16): (a) P(X < 2) (b) P(X > 18) (c) Value x such that P(X < x) = 0.05 (d) Value x such that P(X > x) = 0.95 (a) (b) (c) (d)