For a probability of a random variable x is given below :X: 1 2 4 5 6P: 0.15 0.25 0.2 0.3 0.1What is the Standrard deviation of x ?(a) 1.49(b) 1.56(c) 1.69(d) 1.72

To calculate the standard deviation of a random variable x, we need to follow these steps:

Step 1: Calculate the mean (μ) of x. To find the mean, we multiply each value of x by its corresponding probability and sum them up: μ = (1 * 0.15) + (2 * 0.25) + (4 * 0.2) + (5 * 0.3) + (6 * 0.1) μ = 0.15 + 0.5 + 0.8 + 1.5 + 0.6 μ = 3.55

Step 2: Calculate the variance (σ^2) of x. To find the variance, we need to calculate the squared difference between each value of x and the mean, multiply it by its corresponding probability, and sum them up: σ^2 = [(1 - 3.55)^2 * 0.15] + [(2 - 3.55)^2 * 0.25] + [(4 - 3.55)^2 * 0.2] + [(5 - 3.55)^2 * 0.3] + [(6 - 3.55)^2 * 0.1] σ^2 = [(-2.55)^2 * 0.15] + [(-1.55)^2 * 0.25] + [(0.45)^2 * 0.2] + [(1.45)^2 * 0.3] + [(2.45)^2 * 0.1] σ^2 = [6.5025 * 0.15] + [2.4025 * 0.25] + [0.2025 * 0.2] + [2.1025 * 0.3] + [6.0025 * 0.1] σ^2 = 0.975375 + 0.600625 + 0.0405 + 0.63075 + 0.60025 σ^2 = 2.8475

Step 3: Calculate the standard deviation (σ) of x. To find the standard deviation, we take the square root of the variance: σ = √(2.8475) σ ≈ 1.687

Therefore, the standard deviation of x is approximately 1.69. So, the correct answer is (c) 1.69.