find an example for random variables X,X',Y,Y' with the following characteristics: a)X and X' have the same distribution b)X+Y and X'+Y' have the same distribution c)Y and Y' do not have the same ditribution
Suppose X_n is a sequence of independent Bernoulli random variables and p(X_n=1)=p_n. If Y=∑_(n=1)^∞▒X_n is convergent with probability 1 ,is E(Y) convergent?
Suppose a_n∈ [0,1] and X_n is a sequence of i.i.d random variables with p.d.f : p(X_n=1)= p(X_n= -1)=0.5 . ∑_(n=1)^∞▒a_n X_n is convergent with probability 1, is ∑_(n=1)^∞▒a_n^2 convergent?
A sodium-vapour lamp illuminates, with monochromatic yellow light, two narrow slits that are 1.00 mm apart. if the viewing screen is 1.00m from the slits and the distance from the central bright line to the next bright line is 0.589 mm, what is the wavelength of the light?
If a clock in an airplane is found to slow down by 5 parts in 1013, (i.e., ∆t/∆to = 1.0 + 5.0 × 10. −13), at what speed is the airplane travelling? (Hint: You might need to use an expansion for y)
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