**17)** the sequence is definitely not converging so it doesn't have a limit. but there are 2 limit points 1 and -1.

u can read the difference between limit and limit points.

**26)**f(Ө)= 1/pi ;-pi/2<Ө<pi/2

= 0 ; elsewhere

P(X<x) = P(sinӨ<x) =P(Ө< sin inverse x) = Integral [ x=-pi/2 to x= sin inverse x] 1/pi dӨ = <b>(sin inverse x)/pi + 1/2

**27)**X~N(0, σ²)

(X-0)/ σ² ~ N(0,1)

X^2/ σ² ~ chi square (1) square of standard normally distributed rv is chi square distribution with r =1

so E[X^2/ σ²]=1 mean of chi square is = r (which is 1 in this case)

**E[X^2] = σ²**53)

we know that |x|-|y|<=|x+y|<=|x|+|y|

so |x|-|y|<=|x+y|

replacing y with -y

|x|-|y|<=|x-y|

so (i) is true

(ii) is false. Check with x=2 and y=-3

**54)**It was explained somewhere in this forum quite formally.

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"You don't have to believe in God, but you should believe in The Book." -Paul Erdős