Probability-Tchebycheffs Inequality (ISS Statistics Paper I (Old Subjective Pattern)): Questions 1 - 5 of 5

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Question number: 1

» Probability » Tchebycheffs Inequality

Appeared in Year: 2014

Essay Question▾

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Show that for 40, 000 throws of a balanced coin, the probability is at least 0.99 that the proportion of heads will fall between 0.475 and 0.525.

Explanation

For balanced coin the probability is p = 0.5. For Bernoulli trails where n = 40, 000, the mean and standard deviation is

μ=40, 000×0.5=20, 000

σ=40, 000×0.5×0.5=100

Using Chebyshev’s inequality,

P(Xμ… (83 more words) …

Question number: 2

» Probability » Tchebycheffs Inequality

Appeared in Year: 2013

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Let X be a random variable with E [X] = 4 and E [X 2] = 20. Use Chebyshev’s inequality to determine a lower bound for the probability P [0 < x < 8].

Explanation

Let X be a random variable with mean µ and variance σ 2. Then any k > 0, the Chebyshev’s inequality is

P(Xμkσ)11k2

or P(Xμ<k)>1… (75 more words) …

Question number: 3

» Probability » Tchebycheffs Inequality

Appeared in Year: 2011

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Let X be a positive valued random variable. Prove that

P[Xr]E(X)r,r>0

Hence deduce the Chebychev’s inequality.

Explanation

The expectation of X is define as

E(X)=xf(x)dx

For any x ≥ r

{xr}xf(x)dx

r{xr}… (63 more words) …

Question number: 4

» Probability » Tchebycheffs Inequality

Appeared in Year: 2015

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Let X be a random variable with E [X] = 3 and E [X 2] = 13. Use Chebyshev’s inequality to obtain P [-2 < X < 8].

Explanation

Let X be a random variable with mean µ and variance σ 2. Then any k > 0, the Chebyshev’s inequality is

P(Xμkσ)11k2

or P(Xμ<k)>1… (76 more words) …

Question number: 5

» Probability » Tchebycheffs Inequality

Appeared in Year: 2009

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Let X ~ BIN (100, 0.2). Compute P [10 ≤ X ≤ 30].

Explanation

X ~ BIN (100, 0.2), where n = 100, p = 0.2, q = 0.8

E (X) =np = 20, Var (X) =npq = 16, σ = 4

P[10X30]=P(XE(X)2σ)

Let… (113 more words) …

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