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that is, is phi the distribution function of the standard normal random variable, or is it density function where the cumulative distribution is the integral of phi on the interval (-infinity, t] ? .. I have two text books telling me two different things.

2007-04-08 08:27:31 · 2 answers · asked by ltlbox 1 in Science & Mathematics Mathematics

2 answers

Generally speaking, the lowercase phi (φ) is used for the probability density function whereas the uppercase phi (Φ) is used for the cumulative distribution function.

2007-04-08 09:32:30 · answer #1 · answered by Pascal 7 · 0 0

a million. X~Bin(one thousand,0.4) because of the character of this question we are able to apply the traditional approximation to the binomial P(375<=X<=425) undergo in recommendations that there is a continuity correction because of the fact we are employing a non-provide up distribution to discover discrete opportunities. P(374.5<=X<=425.5) the place X~N(4 hundred, 240) P((374.5-4 hundred)/Sqrt(240)<=Z<=a million.sixty 5) P(-a million.sixty 5<=Z<=a million.sixty 5) = 0.901 the place Z is the traditional commonplace. --------------------------------------... assuming that t3 fairly potential t^3 pdf = 3t^2 2a) E(X) = the fundamental from 0 to a million of 3t^2*t = 3t^3, and the expectancy is 3/4 2b) P(X<0.5) = the fundamental of 3t^2 from 0 to 0.5 = 0.a hundred twenty five --------------- 3. enable X be Alfie and X~U(0,a million) enable Y be Annie and Y~U(0,a million) i've got used a scale conversion because of the fact that's greater basic for me to think of roughly. the question is looking: P[Y>X and X+0.25 > Y] which in words says what's the possibility that Annie arrives after Alfie and interior of 30 minutes (a million/4 of the time for arrival) of Alfie's arrival. the assertion is rewritten as: P[-0.25

2016-10-21 08:58:18 · answer #2 · answered by farraj 4 · 0 0

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