Applied Mathematics for Electrical Engineering  (3130908)

Define the following.

In producing screws, let A mean “screw too slim” and B “screw too small”. Let $\mathrm{P}\left(\mathrm{A}\right)=0.1$ and let the conditional probability that a slim screw is also too small be $\mathrm{P}(\mathrm{B}/\mathrm{A})=0.2$. What is the probability that the screw that we pick randomly from a lot produced will be both too slim and too short?

The joint probability density function of two random variables $\mathrm{x}$ and $\mathrm{y}$ is given by $\mathrm{f}(\mathrm{x},\mathrm{y}) = \left\{\begin{array}{ll}\mathrm{k}(\mathrm{x}+2\mathrm{y}) ;& 0<\mathrm{x}<1 , 0<\mathrm{y}<2\\ 0 ;& \mathrm{elsewhere}\end{array}\right.$. Find the marginal density function of $\mathrm{x}$ and $\mathrm{y}$.

Define the following.

Out of five cars two have tyre problems and one has break problem and two are in good running condition. Two cars are required for the journey. If two cars are selected among five at random and if X denotes the number with tyre problem, Y denotes with break problem then find the marginal probability function of X and Y.