Question

The error of X of certain physical quantity is decided by the density function

a. Determine k that renders f(x) as a valid density function .
b. Find the probability that a random error in measurement is less than 0.5.
c. Find the probability that magnitude of error exceeds 1.

Answer 1

Answer on Question #45516 – Math – Statistics and Probability

The error of X of certain physical quantity is decided by the density function

a. Determine k that renders f(x) as a valid density function.

b. Find the probability that a random error in measurement is less than 0.5.

c. Find the probability that magnitude of error exceeds 1.

Solution:

a. The area under the probability density function must equal one: $\int_{-\infty}^{\infty} f(x) \, dx = 1$

Answer: $k=1$.

b. $p(X \leq 0.5) = \int_{0}^{0.5} f(x) \, dx$

Answer: $\int_{0}^{0.5} f(x) \, dx$.

c. $p(X \geq 1) = \int_{1}^{\infty} f(x) \, dx$

Answer: $\int_{1}^{\infty} f(x) \, dx$.

www.AssignmentExpert.com