[17-10-31]_[1910]_RecitationPlan-upload - O NE-PAGE R EVIEW MATH 1910 Recitation Sections 8.7(Improper Integrals 8.8(Probability \u2022 Integrals with

# [17-10-31]_[1910]_RecitationPlan-upload - O NE-PAGE R...

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O NE -P AGE R EVIEW MATH 1910 Recitation Sections 8.7 (Improper Integrals), 8.8 (Probability) October 31, 2017 Integrals with infinite limits ( improper integrals ) can be defined as follows: Z 1 a f ( x ) dx = ( 1 ) , Z b - 1 f ( x ) dx = ( 2 ) , Z 1 - 1 f ( x ) dx = ( 3 ) If the limit exists, the integral is said to converge , otherwise it diverges . If a is a point of discontinuity of f ( x ) , then we define Z b a f ( x ) dx = ( 4 ) . If b is a point of discontinuity, the integral is defined similarly. A random variable represents a quantity whose value we want to predict. If X is a random variable, the probability that X lies in the interval [ a, b ] is denoted ( 5 ) . A function p ( x ) is called a probability density function (pdf) for a r.v. X if P ( a X b ) = ( 6 ) . A pdf must satisfy ( 7 ) for all x and ( 8 ) . The mean of a random variable X is μ = ( 9 ) . Handout format by Drew Zemke
P ROBLEM S ET MATH 1910 Recitation Sections 8.7 (Improper Integrals), 8.8 (Probability) October 31, 2017 1. Determine whether the following improper integrals converge or diverge.(a)Z10e-cosd(b)Z111(+2)1/3d(c)Z11dq5+2(d)Z12dln2. Verify thatp(x) =54x2is a probability density function on[1, 5]. IfXis the correspondingrandom variable, findP(1X3).3. Find a constantCso thatp(x) =C(2+x)3