f(x) = ²(2-x) for-1 ≤ x ≤ cand f(x) = 0 otherwise.(a) Explaining your work, find the value of the constant c.(b) What is P(X > 1)?(c) Calculate the expectation of X.(d) Calculate the variance of X.C2. For each of the following, (a) calculate the exact value using R; (b) get an approximate value usingan appropriate approximation and without using R. (Statistical tables are available.)(i) P(X ≤ 3), where X~ Bin(1000, 0.005).(ii) P(296 ≤ Y ≤ 307), where Y Bin(1200, 0.25).(iii) P(Z ≥ 398), where Z~ Bin(400, 0.995).

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A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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ƒ(x) = ² (2 − x) for -1 ≤x≤c and f(x) = 0 otherwise. (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.