Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Statistics & Exploratory Data Analysis Probability
Assume that \(X₁, X₂, ..., X₂₅ \)and \(Z₁, Z₂, ..., Z₂₆\) are independent and identically distributed (i.i.d.) random variables with a uniform distribution on the interval [0, 1]. If we denote X(k) and Z(k) as the kth order statistics in the samples X and Z respectively, where k = 8 (the 8th order statistic). What is the correct expression to calculate the probability that X(8) > Z(8)?
1
\(∫_0^1 [25_{C_7} * x^7 (1-x)^{18} * 26_{C_8} x^8 * (1-x)^{18} dx\)
2
\( ∫_0^1[25_{C_8} x^8 * (1-x)^{17} * 26_{C_8} * (1-x)^8 * x^{18}] dx\)
3
\(∫_0^1[25_{C_8} * x^8 * (1-x)^{17} * 26_{C_8} * x^9 * (1-x)^{17}] dx\)
4
\(∫_0^1[25_{C_7} * x^7 * (1-x)^{18} * 26_{C_8} * (1-x)^8 * x^{18}] dx\)
5
Question Not Attempted