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Verify that for a random variable
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Mathematical Methods in the Physical Sciences
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardRecall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .arrow_forwardLet the random variable X be the time in seconds between incoming telephone calls at a busy switchboard. Suppose that a reasonable probability model for X is given by the pdf: fx(x) = { ie for 0arrow_forwardSuppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)arrow_forwardA continuous random variable, X, has the following probability density function. k cos for 0sxs1 f(x)=- for all other values of x (a) Show that k = Find p( x sxs). (b) (c) Find the median 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_forwarde) A random variable X has probability density function (pdf) fx(x), where fx(x) ={ k (2x – x2) 0 < x < 2 0 elsewhere} and k is a constant. Find: k P [ X > 1] iii. the mean of Xarrow_forwardThere are 100 men on a plane. Let x. be the weight (in pounds) of the i th man on the plane. Suppose that the x 's are i.i.d.and E(X)= μ=170, o(X₂)=o=30 Find the probability that the total weight of the men on the plane exceeds 18,000 pounds.arrow_forwardM1arrow_forwardSuppose that therandom variable X has the probability density function c(1– x2) for -1s x <1 f(x) elsewhere What is the variance of Xarrow_forward5. Given a normalized probability density function P(x) of finding the variable x in the interval [x,x + dx], write the definition for a) the mean value (x), b) the variance o? = ((x – (x))?), and c) the standard deviation of the variable x.arrow_forwardQ.2 h(x)==-exp 8 You are given h(x) with the random variable X taking only positive values, -7)+ X 1 X 1 -exp +-expl 2 X 8 24 a. Check if h(x) is a valid pdf (probability density function)? b. Obtain the CDF of X. c. Obtain the mean of X. 4 -exp 80 X 10 ,x≥0arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning