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Answer:
The expected number of days until prisoner reaches freedom is 12 days
Step-by-step explanation:
From the given information:
Let X be the random variable that denotes the number of days until the prisoner reaches freedom.
We can evaluate E(X) by calculating the doors selected, If Y be the event that the prisoner selects a door, Then;
E(X) = E( E[X|Y] )
E(X) = E [X|Y =1 ] P{Y =1} + E [X|Y =2 ] P{Y =2} + E [X|Y =3 ] P{Y =3}
Solving for E[X]; we get
E[X] = 12
Answer:
Step-by-step explanation:
Solution:-
- We are given a parametric form for the vector equation of line defined by ( t ).
- The line vector equation is:
L: < 3 + 2t , t + 1 , 2 -t >
- The same 3-dimensional space is occupied by a unit sphere defined by the following equation:
- We are to determine the points of intersection of the line ( L ) and the unit sphere ( S ).
- We will substitute the parametric equation of line ( L ) into the equation defining the unit sphere ( S ) and solve for the values of the parameter ( t ):
- Solve the quadratic equation for the parameter ( t ):
- Plug in each of the parameter value in the given vector equation of line and determine a pair of intersecting coordinates: