H. W NO 6 Exo1 let (2. A. P) be a probability space for su= [0,1] and A= Band & [ab]c[n] P([a,b])=b-a [0,1] we define (Xn) a Sequance on (2, A, P) 1 0212 no Xn (us= Zn otherwise Prove that XnX almost surly for X(w)= <스 안내드를 o Ex62 Consider a Sequance X Valued In ingan, 2 So how that Xn ⇒o almost surty. EXO3 let ₁.. xn be a seg unce of independent randon Variable Sochthut X = X₂30 and Xen-no² th 23 #slan) P(Xn=0)=1.. D-Show that 1 Snin probability -_-_1_ 37 15 + Su-"Jo Almost sorey ? ngn ket Sus X یا other use P (X₁ = -1) = P(x₂=12) melepdent dontically Exc4 let X₁. & be an distributed valued in 5-113 P(X= -1) = 0,4 P(X= 1) = 0,6 le San M₁4 15 using the central limit theorem find an approximation bo "P(4 (5²6) using the central limit theorem with Continuity Correction find an apprezint to P(45²6) Componce between the two approximation the exact value of P(4(556) using be Exc5 let X₁ Xn and identically distributeuance of independant has a cumulative distribution function F(x). n Define a Sequance F(x)= ^ •[ 11 (x₂) J032] 6=1 (1 WEA where 11 (w), A lo othense show that Fn(2) F(x) in probability is Fn(2) F(2) Almost sorry
