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Expectation of a random variable

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A doctor advices a patient to go on a particular diet for 2 weeks. Considering the general condition of the patient, the amount of weight the patient may loose is assumed to be between 5 Kg and 10 Kg, and all the amounts are felt equally likely. Find the expected lose of weight

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Solution describes the method to find the expectation of a random variable.

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Compute the expectation of random variables.

Exercise 1:
Let Y be a random variable with normal distribution with mean (μ =2), and standard deviation (σ = 1). Let J(t) = Y I[1,∞)(t). (I =1 in the interval [1,∞), and 0 otherwise). Define a new random variable L by putting that L is equal to integral from minus infinity to plus infinity e^t dJ(t). Compute the expectation of L.

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