Question

A group of engineers have developed a sophisticated radar system called (MTD). The system was used to successfully detect aircraft embedded in ground clutter. The researchers show that the magnitude Y of the Doppler frequency of a radar-received signal obeys a Weibull distribution with parameters a=2, and B-4. Find E(Y)

Answer 1

The expected value E(Y) of the Weibull distribution with parameters a=2, and B=4 is approximately 5.0132.The result is that the expected magnitude of the Doppler frequency E(Y) is approximately 5.0132.

Step-by-step explanation:

The student is asking about the expected value E(Y) of a Weibull distribution, which is a statistical distribution commonly used in reliability engineering and weather forecasting.

The expected value of a Weibull distribution with shape parameter a and scale parameter B is given by the formula:

• E(Y) = B * Gamma(1 + 1/a)

Where Gamma represents the gamma function. In our case, the shape parameter a is 2 and the scale parameter B is 4. Therefore, the expected value E(Y) can be calculated as follows:

• E(Y) = 4 * Gamma(1 + 1/2)
• E(Y) = 4 * Gamma(1.5)
• E(Y) = 4 * (√π/2)
• E(Y) = 4 * 1.2533...
• E(Y) ≈ 5.0132

The result is that the expected magnitude of the Doppler frequency E(Y) is approximately 5.0132.