Explanation Formula used: The function u and v differentiable then, ∫ u v d x = u ∫ v d x − ∫ [ d d x ( u ) ∫ v d x ] d x . Calculation: The probability density function for the exponential distribution is defined by, f ( x ) = a e − a x for x in [ 0 , ∞ ) . The expected value is calculated as follows. μ = ∫ 0 ∞ x a e − a x d x = [ − x e − a x ] 0 ∞ − ∫ 0 ∞ ( − e − a x ) d x ( by above Formula ) = [ − ∞ e − a × ∞ + 0 × e − a × 0 ] + [ − e − a x − a ] 0 ∞ ( ∵ e − ∞ = 0 , e 0 = 1 ) = 0 − 1 a [ e − a × ∞ − e − a × 0 ] = 1 a The variance is var ( X ) = ∫ 0 ∞ x 2 e − a x d x − ( 1 a ) 2 . Use integration by parts to solve the above integral ∫ x 2 e − a x d x . ∫ x 2 e − a x d x = ∫ x ( x e − a x ) d x = x ( − x e − a x − 1 a e − a x ) − ∫ ( − x e − a x − 1 a e − a x ) d x ( by previous

Calculus with Applications Books a la Carte Edition

11th Edition

ISBN: 9780133864564

Author: Margaret L. Lial; Nathan P. Ritchey; Raymond N. Greenwell

Publisher: Pearson Education

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Chapter 11, Problem 8RE

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Whether the statement “For an exponential random variable, the expected value and standard deviation are always equal” is true or false.

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Chapter 11, Problem 7RE

Chapter 11, Problem 9RE

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There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three investment? STEP 1: The formula for compound interest is A = nt = P(1 + − − ) n², where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to A = Pert Find r and n for each model, and use these values to write A in terms of t for each case. Annual Model r=0.10 A = Y(t) = 1150 (1.10)* n = 1 Quarterly Model r = 0.10 n = 4 A = Q(t) = 1150(1.025) 4t Continuous Model r=0.10 A = C(t) =…

Chapter 11 Solutions

Calculus with Applications Books a la Carte Edition

Ch. 11.1 - YOUR TURN 1 Repeat Example 1(a) for the function...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 1WE Ch. 11.1 - Prob. 2WE Ch. 11.1 - Prob. 3WE Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...

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