"Frequency agile tracking radars have received considerable attention in the literature. Frequency agility is useful in reducing target scintillations, thereby reducing tracking errors under certain conditions. However, little attention has been devoted to the improvement that can be expected in target detection with a frequency agile radar. In the past, complete pulse-to-pulse decorrelation of the target returns has been assumed for all of the analyses concerning target detection with frequency agile radars. This assumption always implies a transmitter with a large bandwidth. This dissertation analyses a pulsed non-coherent frequency agile radar applied to Swerling's Case I target. The target model is modified by assuming time decorrelation of the returns in the latter portion of the dissertation. Partial correlation of the returns is also allowed. It is shown that random selection of the transmitted frequency from a continuous probability density function yields a significant reduction in the transmitter bandwidth requirement, when compared to previous analyses, with a negligible decrease in detection range. Two practical density functions for the transmitted frequency are studied in detail, the uniform and anti-sine distribution. However, the results are general in that the curves for detection probabilities may be applied directly to any pulsed non-coherent frequency agile radar whose transmitted frequency is obtained from a probability density function. The analysis yields a closed form solution, previously unknown, for detection probabilities in the case of Swerling's Case I target. A computer program is included which calculates detection probabilities for Swerling's Case I target modified by a time decorrelation function"--Abstract, leaves ii-iii.