5. The force  applied to a pole has components acting along the  axes. If the distribution of the magnitude of F follows a normal distribution , and  and . Determine the distributions of the magnitudes of its three components.

 

Solution

For  and , the above equation is

We get  

For , we have

                                                          

                                                          

                                                          

                                                          

Thus, we can conclude

                                                                                                              Ans.

                                                                                                        Ans.

                                                                                                           Ans.