Question

1) In this exercise, we are given the distribution of Sn=U1+U2+…+Un, where Ui are i.i.d. Uniform(a=0,b=1) random variables.

a) Find the p.d.f. of S3=U1+U2+U3 and sketch its graph.

b) Find the p.d.f. of S4=U1+U2+U3+U4 and sketch its graph

c) Neither S3 or S4 are distributions with a name, but if you sketch their p.d.f.s, they should resemble a previous distribution. Which one?

Answer 1

distribution , coniche further extension distribution is Quassion Here give given vi are i-id uniform (011). The sum of n iind uniform coil) random variables Irwin Hall distribution is pdf of Sa= Uitu2 +03 f(1/2) x2 fx(x) = (112) Q-22²+6x-3) (12)( 2-3) 2 1 casa 25253 6 pdf of S4 = UI+U2+ U3+04 1 (16) 23 fx (2) = (116) (-3x²122²_122+4) leaca (116) (3 x 324 r²+604-44) 26463 (Pro) (-x+472 3 <xea Graph (b) pdf Graph ca pdf yaxis 1 1- n=4 n=3 0.6 0.6 0.4+ 0.47 02 0.21 2 4 2 af 10 mean median = modes 8 means median model, 5. ode = 2 - 4 22 CIf we look towards the graph, grophis doe symmet REDMI NOTE 8 istributions are similar to bates distribution bates AI QUAD CAMERA have