Statistics Question
Assignment II STATISTICS AND PROBABILITY [262 MATH-3] Academic Year 2023-24 G, 1444-45 H Third Semester DEPARTMENT OF MATHEMATICS COLLEGE OF SCIENCE, Jazan University, KSA 262 MATH-3_Third Semester_2023-2024 Name I.D. Group Number 262 MATH-3_Third Semester_2023-2024 Q 1 If π is a random variable with distribution π: 0 1 2 3 π(π): 1 1 1 1 4 4 4 4 Find the mean, Variance and standard deviation. Q 2 If π is a random variable with distribution π: 0 1 2 3 4 π(π): 0 πΎ 2πΎ 3πΎ 4πΎ Explain the following: (i) For which value of πΎ, π(π) is probability mass function? (ii) Find the following probabilities: (a) π(1 ≤ π < 4). (b) π(2 < π ≤ 4). Q 3 A box contains 6 balls. Two are numbered 4, two are numbered 5, and two are numbered 6. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the variance (π 2 ) and standard deviation (π) of the numbers on the balls. Q 4 A special six-sided die is made in which 2 sides have 6 spots, 3 sides have 4 spots, and 1 side has 1 spot. If the die is rolled, find the expected value of the number of spots that will occur. Q 5 Let π~π΅(4, 0.6). Find the following (i) (ii) (iii) π(π = 2) π(1 < π < 4) Also find mean and variance. Q 6 Let π~π(2). Find the following (i) (ii) (iii) π(π = 0; 2) π(π = 2; 2) Also find mean and variance. 262 MATH-3_Third Semester_2023-2024 Q 7 From the paired data: π 1 2 3 4 5 π 10 8 12 12 16 (i) Find the correlation coefficient (π). (ii) Explain the relationship. (iii) Find the line of regression. (iv) Estimate the value of π when π = 5. Q 8 Find the following probabilities or area. (i) π(π§ < 1.23) (ii) π(π§ > 1.37) (iii) π(1.45 < π§ < 1.62) (iv) π(π§ < −1.42) (v) π(−1.34 < π§ < 2.15) Q 9 From the paired data set (π, π): (5,9), (4, 7), (3, 5), (2,3), (1, 1) (i) Find the correlation coefficient (π). (ii) Explain the relationship. (iii) Find the line of regression. (iv) Estimate the value of π when π = 10. Q 10 If π is a normal random variable with mean 4 and variance 25, then find the standard normal variate z for the following data: (i) π = 10 (ii) π = 3. 262 MATH-3_Third Semester_2023-2024
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