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Probability and StatisticsQuestion and Answers: Page 3
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Question and Answers Forum |
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Probability and StatisticsQuestion and Answers: Page 3 |
| (3/2)cos^(−1) (√(2/(2+π^2 )))+(1/4)sin^(−1) ((2(√(2π)))/(2+π^2 ))+tan^(−1) ((√2)/π) |
| The probability density function f(x) of a variable x is given by f(x)= { ((kxsin πx 0≤x≤1)),((0 for all value of x)) :} Show that k=π and deduce that mean and the variance of the distribution are (1−(4/π^2 )) and (2/π^2 )(1−(8/π^2 )) |
| Find the first four moment of the binomial distribution |
| Show that E(Z)=0 and Var(Z)=1 where Z is the standard normal variable |
| If θ be the acute angle between two regression line in the case of two variables x and y Show that tan θ=((1−r)/r).((σ_x σ_y )/(σ_x ^2 +σ_y ^2 )) where r,σ_x ,σ_y have their usual meanings. Explain the significance where r=0 and r=±r 1/2/2024 |
| Establish the formular σ_(x−y) ^2 =σ_x ^2 +σ_y ^2 −2rσ_x σ_y where by r is the correlation coefficient between x and y 1/2/2024 |
| prove that. 0!=1 |
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| It is known that the set A={1 , 2, 3, ..., 100} The numbers of subsets of A which when added together are divisible by 4 |
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| A man has equal chances of travelling by air(A), bus(B) and train(T). the probability that when he travels by air, bus or train he will have an accident are (1/3), (3/5) and (1/(10)). find the probability that (a) he travelled and was involved in an accident (b) he was travelling by air given that he was involved in an accident. (c) he was travelling by bus or he arrived safely |
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| suppose that a sample of size n=8 is drawn from a population with PDF: {f(x)=(x^2 /9), 0 < x < 3} find (1) p(1 < x < 2) (2) PDF and CDF of the fourth smallest O.S |
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