On unbiased estimation of $P(Y<X)$ in normal case

Under assumption that normally distributed random variables $X$ and $Y$ are independent new expressions for minimum variance unbiased estimates of the probability $P(Y<X)$ have been obtained. These estimates are given for two cases: - when distribution of $Y$ is comletely specified and when all parameters of the distributions of $X$ and $Y$ are unknown. The last estimate is nore suitable for practical applications than that of Downton [3].