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- Write properties of mathematical expectation.
- Define random variable.
- Define Binomial distribution.
- Define Normal distribution.
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- Define null hypothesis.
- Define alternative hypothesis.
- Write properties of correlation and regression.
- What is the coefficient of determination?
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PART – B (3 x 16 = 48 Marks)
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Two dice are thrown. Let X assign to each point (a, b) in S the maximum of its numbers i.e., X(a, b) = max(a, b). Determine the probability distribution for X.
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A random variable X has the following probability function:
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x 0 1 2 3 4 5 6 7 P(x) 0 k 2k 2k 3k k2 2k2 7k2+k - Find k
- Evaluate P(X < 6), P(X ≥ 6) and P(0 < X < 5)
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The height of six randomly chosen sailors are (in inch): 63, 65, 68, 69, 71, 72. Those of 10 randomly chosen soldiers are 61, 62, 65, 66, 69, 69, 70, 71, 72, 73. Discuss, in the light of these data, whether the sailors are on the average taller than soldiers.
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Genetic theory states that children having one parent of blood type A and the other of blood type B will always be of one of the three types A, B, AB and that the proportion of these types will on average be as 1:2:1. A report states that out of 300 children having one A parent and one B parent, 80 were type A, 135 type B and 85 type AB. Test the hypothesis by χ2-test.
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Obtain the rank correlation coefficient from the following data:
x 68 64 75 50 64 80 75 40 55 64 y 62 58 68 44 81 60 68 48 50 70
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