Probability Distributions

What is a random variable in probability?

• A fixed number

• A variable that always increases

• A variable that takes numerical values based on outcomes of a random experiment

• A constant outcome

What does a probability distribution function (p.d.f) represent?

• The most frequent outcome

• Probabilities for all possible outcomes of a random variable

• Total number of outcomes

• The average of all outcomes

What is expected value?

• The maximum value

• The value most likely to occur

• The weighted average of all outcomes

• The median of data

Why do earthquakes commonly occur in Japan?

• It's close to the equator

• It lies on major tectonic plate boundaries

• It has a large population

• It gets heavy rainfall

What can cause bias in exit poll results?

• Random sampling

• Equal voting

• Selective surveying or non-representative sample

• Counting error

A store sells 3 products with the following probability of sales in a week: Product A = 0.4, B = 0.35, C = 0.25. If profit per sale is ₹100, ₹200 and ₹150 respectively, what is the expected profit?

• ₹150

• ₹165

• ₹120

• ₹180

How can expected value help in inventory management?

• By ensuring only high-value items are ordered

• By estimating average sales to plan stock

• By guessing what customers like

• By reducing all costs

What is the primary objective of the Swachh Bharat Mission?

• To provide piped drinking water

• To improve sanitation and cleanliness across India

• To build rural roads

• To increase agricultural output

In a survey, expected number of recyclers per family is 2.5. What can planners use this for?

• Predicting plastic production

• Estimating daily food consumption

• Estimating bins or collection services needed

• Planning festivals

How can we relate expected number of recyclers to Swachh Bharat goals?

• It encourages spending

• It promotes digital literacy

• It helps estimate and manage local waste resources

• It improves attendance