Let X Be an Exponential Random Variable With $\lambda$ = 250 Find the Following Probabilities

question 110

Essay

Let X be an exponential random variable with $\lambda$ = 2.50. Find the following probabilities.
a. P(X $\geq$ 1.5).
b. P(X $\leq$ 1).
c. P(0.25 $\leq$ X $\leq$ 0.78).
d. P(X = 0.41).

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Definitions:

Taxes

Obligatory charges imposed by the government on the earnings of employees, profits of companies, or included in the prices of various goods, services, and transactions.

Income Tax

A tax levied by governments on individuals or entities based on their income or profits.

Taxable Income

The amount of income subject to taxes, after deductions and exemptions, according to the tax laws governing the taxpayer.

Tax Rate

The percentage at which an individual or corporation is taxed by the government on income, property, or sales.