Distribution of Major Hurricanes y 0 1 2 3 4 P(Y = y) y 0.182 5 0.284 6 0.264 7 0.071 8 0.033 Print P(Y=y) 0.045 0.025 0.009 0.087 Done is, the two-standard-deviation interval is places as needed. Use ascending order.) ar

(a) The mean of the probability distribution of a random variable is calculated using the formula, 

µ = Σ y_iP(Y = y_i) 

Using the above formula we have, 

µ = 0×P(Y = 0) + 1×P(Y = 1) + 2×P(Y = 2) + 3×P(Y = 3) + 4×P(Y = 4) + 5×P(Y =5) + 6×P(Y =6) + 7×P(Y = 7)+ 8×P(Y = 8)

On substituting the values we get 

µ = 0×0.182 + 1×0.284 + 2×0.264 + 3×0.071 + 4×0.033 + 5×0.045 + 6×0.025 + 7×0.009 + 8×0.087

µ = 0 + 0.284 + 0.528 + 0.213 + 0.132 + 0.225 + 0.15 + 0.063 + 0.696

µ = 2.291

Since, µ is known as the mean or average of the distribution hence, the correct option is The average number of major hurricanes per year is 2.291 hurricane.