On the Relationship between the Conditional and Unconditional Distribution of a Random Variable

This paper studies the relationship between the unconditional and conditional distribution of the same random variable, say Y, when the distribution of the conditioning random variable X is of a known form. The problem is tackled in the general case where the distribution of Y and Y given X are mixed. Attention is focused to two particular cases. In the first X is assumed to follow a Poisson distribution; in the second X is allowed to have a mixed Poisson form. Potential applications are also discusse

The effect of arm training on thermoregulatory responses and calf volume during upper body exercise

The final publication is available at Springer via https://doi.org/10.1007/s00421-014-2842-9.PURPOSE: The smaller muscle mass of the upper body compared to the lower body may elicit a smaller thermoregulatory stimulus during exercise and thus produce novel training-induced thermoregulatory adaptations. Therefore, the principal aim of the study was to examine the effect of arm training on thermoregulatory responses during submaximal exercise. METHODS: Thirteen healthy male participants (Mean ± SD age 27.8 ± 5.0 years, body mass 74.8 ± 9.5 kg) took part in 8 weeks of arm crank ergometry training. Thermoregulatory and calf blood flow responses were measured during 30 min of arm cranking at 60% peak power (W peak) pre-, and post-training and post-training at the same absolute intensity as pre-training. Core temperature and skin temperatures were measured, along with heat flow at the calf, thigh, upper arm and chest. Calf blood flow using venous occlusion plethysmography was performed pre- and post-exercise and calf volume was determined during exercise. RESULTS: The upper body training reduced aural temperature (0.1 ± 0.3 °C) and heat storage (0.3 ± 0.2 J g(-1)) at a given power output as a result of increased whole body sweating and heat flow. Arm crank training produced a smaller change in calf volume post-training at the same absolute exercise intensity (-1.2 ± 0.8% compared to -2.2 ± 0.9% pre-training; P < 0.05) suggesting reduced leg vasoconstriction. CONCLUSION: Training improved the main markers of aerobic fitness. However, the results of this study suggest arm crank training additionally elicits physiological responses specific to the lower body which may aid thermoregulation.Peer reviewedFinal Accepted Versio