Please Help solve the advanced Probability Question:

Our friend visits us. We know that the duration of her visit was randomly chosen between zero and her favorite number (some positive number). We do not know her favorite number but we estimate it using that her visit was exactly x minutes. Our estimate will simplyir be cx, where c is an appropriately chosen positive number. Then 0 the correct value etc ensures that our estimate is unbiased and has minimal mean squared error. 0 c=2 is a better chose than c=1.5 in every respect. 0 we should choose the c that gives the smallest vananoe for our estimator. O the correct value etc can guarantee that our estimate is unbiased, but then it won't have the minimal mean squared error