Pls answer the three parts with correct solutions Suppose the random variable Y counts the number of heads in 10 tosses of a biasedcoin with P(H) = 0.6 and P(T) = 0.4 on each toss. Y then has a binomial distribution:it can take on the integer values 0 through 10, each with with probability P(Y = y)10 0.66 and variance V(X) =1.(¹0) 0.6 0.4¹0-y. It also has expected value E(X)10.0.6 0.4 2.4..=a. Work out P (Y− 6| > 3) as precisely as you can.Chebyshev's Inequality, which we'll see in class later on, lets us estimate probabilitiesinvolving random variables knowing nothing about the distribution involved except forits expected value and standard deviation. Mind you, these estimates are usually prettycrude, but they are pretty easy to get.There are several ways to state this inequality; one common version states that arandom variable X, which could be discrete or continuous, with expected value μ = : E(X)and standard deviation σ = √V(X) must satisfyP(|X − µ| ≥ ko) ≤C.=1k²for any real number k > 0. Technically, this form of Chebyshev's Inequality gives us upperbounds for certain probabilities.If the mean and/or the standard deviation are not defined or are unknown for X,Chebyshev's Inequality isn't useful. Note also that it is of interest only if k > 1, since if1k≤ 1, then ≥ 1 and any probability must be ≤ 1.k²b.Use Chebyshev's Inequality to find an upper bound for the probability P (|Y − 6| > 3)in question 1. How close is this upper bound to the precise value?Either findi. a probability density function f(x) for a continuous random variable such that== 0, o = 1, anda continuous random variable X with this density will have μsatisfy P (|X| ≥ 2) = ½, orii. a probability distribution function m(x) for a discrete random variable X suchthat a discrete random variable X with this distribution function will have μ = 0,= 1, and satisfy P(|X| ≥ 2) = ¹.0 =

Y is a random variable that can take on values from 0 to 10 with probability P(Y=y) =E(Y) =6 and…

Suppose the random variable Y counts the number of heads in 10 tosses of a biased coin with P(H) = 0.6 and P(T) = 0.4 on each toss. Y then has a binomial distribution: it can take on the integer values 0 through 10, each with with probability P(Y = y) (10) 0.6⁹ 0.4¹0-y. It also has expected value E(X) = 10.0.6 = 6 and variance V(X) = 10.0.6.0.4 2.4. = = a. Work out P(|Y6| > 3) as precisely as you can. Chebyshev's Inequality, which we'll see in class later on, lets us estimate probabilities involving random variables knowing nothing about the distribution involved except for its expected value and standard deviation. Mind you, these estimates are usually pretty crude, but they are pretty easy to get.