2020年3月12日 · 3.199 E +01 is the equivalent of 3.199 ×101 3.199 × 10 1. The 3.199 3.199 part is the mantissa, E stands for exponential, and +01 + 01 is the exponent (in base 10). The number is should like this on some calculators as they cannot display superscript.

For a random variable X, E(X2) = [E(X)]2 iff the random variable X is independent of itself. This follows from the property of the expectation value operator that E(XY) = E(X)E(Y) iff X and Y are independent random variables.

The answer obviously must contain all the powers of xk for 0 ≤ k ≤ n so the solution can't be much simpler than this. E.g. for x> 0 you might try ((− ∂α)n∫ e − αx)|α = 1 but now you have to differentiate n times so this is essentially the same thing.

2016年7月19日 · I want to understand something about the derivation of $\\text{Var}(X) = E[X^2] - (E[X])^2$ Variance is defined as the expected squared difference between a random variable and the mean (expected v...

I got a problem of calculating E[eX], where X follows a normal distribution N(μ, σ2) of mean μ and standard deviation σ. I still got no clue how to solve it. Assume Y = eX. Trying to calculate this value directly by substitution f(x) = 1 √2πσ2e − (x − μ)2 2σ2 then find g(y) of Y is a nightmare (and I don't know how to calculate this integral to be honest). Another way is to find ...

2017年4月8日 · For $$e^ {-j\pi n}$$ How does this become $$ (-1)^n$$ or is it actually $$ (-1)^ {-n}$$ I have checked on calculator and values are all the same when the same n value ...

2017年4月19日 · I understand that multiplying by i is equivalent to rotating the position vector of the complex number in Argand Plane by 90 degrees anti-clockwise. How can rotating i anti-clockwise i number of times give e − π / 2? So can somebody explain to me graphically or more intuitively, how ii = e − π / 2 ?

2020年9月29日 · Assuming that ez e z is defined as ∑ n=0∞ zn n! ∑ n = 0 ∞ z n n! (remember that there are a few ways of defining e e), we have:

2014年3月16日 · Prove that e is an irrational number. Recall that e = ∞ ∑ n = 0 1 n!, and assume e is rational, then ∞ ∑ k = 0 1 k! = a b, for some positive integers a, b.

2014年10月28日 · I read that e = ∑∞i = 0 1 n!. This isn't immediately obvious to me, and I can't find proof of this. Can somebody explain to me, how do I prove this from definition e = limn → ∞(1 + 1 n)n, or point me to one?