[R] Trying to get around R

[Epselon]

I have three problems I am trying to simulate, that I am having difficulty
getting around with.

Problem 1. 
I want to determine the 85 percentile (the x value for which the sum of
probabilities becomes 0.85) of the following distributions (two binomials
and a Poisson with rate Lmbda= np of the two binomials): X ~B(10, 0.3),
Y~P(3) , 
Z~B(30, 0.1). I want to show that  that Y is a good approximation for Z but
not for X...(by examining these distributions for few
different percentiles)

Problem 2:
For a binomial distribution X ~ B(20, 0.4), I want to use R to calculate
P{|X − μ| < 2} and verify that it is near or larger than 0.95. (Hint from
the text book: Since μ = 8 and   2.3 then you may want to read the
weights, or probabilities, of the values 6:10, into a vector v and then use
the command sum(v) to
calculate the sum.) Repeat this for another set of parameters of your
choice.

Problem 3:
Draw a sample of size 10, from a Poisson with Lambda= 5, and calculate the
mean and the standard deviation of this sample, Repeat this calculation with
size 20 and 30 and demonstrate
that ¯X gets closer to μ as the sample size increases.

Thanks.

I would appreciate it if someone accompanied the codes with a brief
explanation so I can be able to replicate it myself. 
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