What is the cumulative distribution function of the standard normal random variable?

Answer 1

This function is denoted by F(x) is the integral from -inf to x of the the probability density function f(x) for the normal distribution. See textbooks for details.

Answer 2

a million. X~Bin(1000,0.4) because of nature of this question we are waiting to coach the classic approximation to the binomial P(375<=X<=425) submit to in techniques that there is a continuity correction because of actuality we are using a non-furnish up distribution to locate discrete opportunities. P(374.5<=X<=425.5) the situation 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 situation Z is the classic primary. --------------------------------------..... assuming that t3 extremely ability t^3 pdf = 3t^2 2a) E(X) = the standard from 0 to a million of 3t^2*t = 3t^3, and the expectation is 3/4 2b) P(X<0.5) = the standard of 3t^2 from 0 to 0.5 = 0.one hundred twenty 5 --------------- 3. enable X be Alfie and X~U(0,a million) enable Y be Annie and Y~U(0,a million) i've got have been given used a scale conversion because of incontrovertible fact it is larger basic for me to think of of roughly. the question is finding: P[Y>X and X+0.25 > Y] which in words says what's the prospect that Annie arrives after Alfie and indoors of half-hour (a million/4 of the time for arrival) of Alfie's arrival. the very fact is rewritten as: P[-0.25

Answer 3

It's a difficult integral to do. It involves a change of coordinates to polar and doing the square. That's why the cdf is in tables.

Answer 4

see: http://en.wikipedia.org/wiki/Normal_distribution