Suppose there are two manufacturers A and B of a smartphone battery Company A manufactures the fraction of 60% of all the batternes used in the smartphones while company B manufactures the rest Assume that the hfetime of each battery is a continuous random variable T (with parameterX>0) whose probabilıty density function is given by 了(1-) for 0 ntS> fa(t) = %3D otherwise The parameter A depends on the manufacturer of the battery If the battery is manufactured by A then A =1 while if it is manufactured by B then = 2 Suppose you buy a new smartphone that is randomly picked among all the produced phones Compute the expectation and variance of the lifetime of the battery of your new phone Hınt In calculatıng the expectation and variance you should condition on the manufacturer of the battery

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.