In March 1995 the Space Shuttle Carried an Experiment Designed $p(x)=x e^{-x}$

question 10

Short Answer

In March 1995 the space shuttle carried an experiment designed by a Harvard student who studies the growth of crystals.Suppose the probability density function of the length, x cm, of a crystal grown in space is modeled by $p(x)=x e^{-x}$ for $x \geq 0$ .The cumulative distribution function giving the probability that a crystal has length $\le$ t cm is represented by P(t).What is the mean crystal length that this model predicts? Give your answer to two decimal places.

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Definitions:

Risk-Free Asset

An investment expected to return its original value without any loss and with absolute certainty, typically associated with government bonds.

Market

A place or system where buyers and sellers interact to trade goods, services, or financial instruments.

Expected Return

The anticipated amount of profit or loss an investment is likely to generate over a specific period.

Stock X

An online marketplace and clothing reseller, primarily of sneakers and streetwear.