Question 1. The 2020 UDHS reported the number per household being a certain size. The data isin table below ("Households by age")Size ofhousehold1 2 3 4 5 6 >7Probability 1.5% 2.4% 6.3% 13.7% 26.7% 33.6% 15.8%a) Draw a histogram of the probability distributionb) Calculate the mean, variance and standard deviation for the discrete probability distributionc) Is it unusual for a household to have 2 people in the family?d) If you did come across a family of two people, what would you think?

a) To draw a histogram of the probability distribution, we will use the data provided in the table. The x-axis will represent the size of the household, and the y-axis will represent the probability. We will plot each size of the household on the x-axis and the corresponding probability on the y-axis.

b) To calculate the mean, variance, and standard deviation for the discrete probability distribution, we will use the formula:

Mean = Σ (x * P(x)) Variance = Σ ((x - Mean)^2 * P(x)) Standard Deviation = √Variance

where x represents the size of the household and P(x) represents the probability of that size of the household.

c) To determine if it is unusual for a household to have 2 people, we can compare the probability of a household size of 2 with the probabilities of other household sizes. If the probability of a household size of 2 is significantly different from the other probabilities, then it can be considered unusual.

d) If we come across a family of two people, we can infer that the probability of this household size is 2.4%. However, we should also consider other factors such as the context and the specific population being studied before making any conclusions.

a) To draw a histogram of the probability distribution, we will use the data provided in the table. The x-axis will represent the size of the household, and the y-axis will represent the probability. We will plot each size of the household on the x-axis and the corresponding probability on the y-axis.

b) To calculate the mean, variance, and standard deviation for the discrete probability distribution, we will use the formula:

Mean = Σ (x * P(x)) Variance = Σ ((x - Mean)^2 * P(x)) Standard Deviation = √Variance

where x represents the size of the household and P(x) represents the probability of that size of the household.

c) To determine if it is unusual for a household to have 2 people, we can compare the probability of a household size of 2 with the probabilities of other household sizes. If the probability of a household size of 2 is significantly different from the other probabilities, then it can be considered unusual.

d) If we come across a family of two people, we can infer that the probability of this household size is 2.4%. However, we should also consider the context and other factors before making any conclusions.